1,0,-1,95,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3))/cos(c + d*x)^2, x)","F"
2,0,-1,92,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3))/cos(c + d*x),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3))/cos(c + d*x), x)","F"
3,0,-1,88,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3), x)","F"
4,0,-1,89,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3), x)","F"
5,0,-1,93,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3), x)","F"
6,0,-1,95,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3))/cos(c + d*x)^2, x)","F"
7,0,-1,92,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3))/cos(c + d*x),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3))/cos(c + d*x), x)","F"
8,0,-1,90,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3), x)","F"
9,0,-1,91,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3), x)","F"
10,0,-1,91,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3), x)","F"
11,0,-1,95,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(1/3)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(1/3)), x)","F"
12,0,-1,92,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(1/3)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(1/3)), x)","F"
13,0,-1,90,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(1/3), x)","F"
14,0,-1,88,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(1/3),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(1/3), x)","F"
15,0,-1,93,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(1/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(1/3), x)","F"
16,0,-1,95,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)), x)","F"
17,0,-1,92,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)), x)","F"
18,0,-1,90,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(4/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(4/3), x)","F"
19,0,-1,90,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(4/3),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(4/3), x)","F"
20,0,-1,93,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(4/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(4/3), x)","F"
21,0,-1,146,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3)*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(4/3)*(1/cos(c + d*x))^m, x)","F"
22,0,-1,146,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^m, x)","F"
23,0,-1,144,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^m, x)","F"
24,0,-1,147,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(1/3),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(1/3), x)","F"
25,0,-1,145,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(2/3),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(2/3), x)","F"
26,0,-1,148,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(4/3),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(4/3), x)","F"
27,0,-1,145,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^m, x)","F"
28,0,-1,120,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/cos(c + d*x)^2, x)","F"
29,0,-1,109,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/cos(c + d*x),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/cos(c + d*x), x)","F"
30,0,-1,113,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n,x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n, x)","F"
31,0,-1,117,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n,x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n, x)","F"
32,0,-1,132,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n,x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n, x)","F"
33,0,-1,132,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n,x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n, x)","F"
34,0,-1,142,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(5/2), x)","F"
35,0,-1,142,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(3/2), x)","F"
36,0,-1,140,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(1/2), x)","F"
37,0,-1,141,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(1/2), x)","F"
38,0,-1,140,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(3/2), x)","F"
39,0,-1,142,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(5/2), x)","F"
40,0,-1,167,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^m,x)","\int \left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(b/cos(c + d*x))^n*(1/cos(c + d*x))^m, x)","F"
41,0,-1,154,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
42,0,-1,151,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x), x)","F"
43,0,-1,146,0.000000,"\text{Not used}","int((b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
44,0,-1,148,0.000000,"\text{Not used}","int(cos(c + d*x)*(b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
45,0,-1,150,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
46,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
47,0,-1,154,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
48,0,-1,151,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x), x)","F"
49,0,-1,146,0.000000,"\text{Not used}","int((b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
50,0,-1,146,0.000000,"\text{Not used}","int(cos(c + d*x)*(b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
51,0,-1,150,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
52,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(b/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
53,0,-1,154,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)), x)","F"
54,0,-1,147,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)), x)","F"
55,0,-1,142,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(2/3), x)","F"
56,0,-1,147,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)), x)","F"
57,0,-1,154,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)), x)","F"
58,0,-1,154,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(b/cos(c + d*x))^(2/3)), x)","F"
59,0,-1,154,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)), x)","F"
60,0,-1,149,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)), x)","F"
61,0,-1,146,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(4/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(b/cos(c + d*x))^(4/3), x)","F"
62,0,-1,149,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)), x)","F"
63,0,-1,154,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)), x)","F"
64,0,-1,154,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(b/cos(c + d*x))^(4/3)), x)","F"
65,0,-1,230,0.000000,"\text{Not used}","int((b/cos(c + d*x))^(4/3)*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^(4/3)*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
66,0,-1,227,0.000000,"\text{Not used}","int((b/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
67,0,-1,225,0.000000,"\text{Not used}","int((b/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
68,0,-1,228,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(1/3),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(((1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(1/3), x)","F"
69,0,-1,226,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(2/3),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int(((1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(2/3), x)","F"
70,0,-1,234,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(4/3),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int(((1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(b/cos(c + d*x))^(4/3), x)","F"
71,0,-1,226,0.000000,"\text{Not used}","int((b/cos(c + d*x))^n*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^n*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
72,0,-1,189,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
73,0,-1,182,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x), x)","F"
74,0,-1,175,0.000000,"\text{Not used}","int((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
75,0,-1,191,0.000000,"\text{Not used}","int(cos(c + d*x)*(b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
76,0,-1,208,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
77,0,-1,208,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
78,0,-1,223,0.000000,"\text{Not used}","int((b/cos(c + d*x))^n*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^n*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
79,0,-1,223,0.000000,"\text{Not used}","int((b/cos(c + d*x))^n*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^n*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
80,0,-1,221,0.000000,"\text{Not used}","int((b/cos(c + d*x))^n*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((b/cos(c + d*x))^n*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
81,0,-1,222,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
82,0,-1,221,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
83,0,-1,223,0.000000,"\text{Not used}","int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((b/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
84,1,201,140,5.192160,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+3\,C\right)}{4\,d}-\frac{\left(A\,a+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{10\,A\,a}{3}-\frac{13\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,a}{3}+\frac{116\,C\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{22\,A\,a}{3}-\frac{19\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(4*A + 3*C))/(4*d) - (tan(c/2 + (d*x)/2)*(3*A*a + (13*C*a)/4) + tan(c/2 + (d*x)/2)^9*(A*a + (3*C*a)/4) - tan(c/2 + (d*x)/2)^7*((10*A*a)/3 + (13*C*a)/6) - tan(c/2 + (d*x)/2)^3*((22*A*a)/3 + (19*C*a)/6) + tan(c/2 + (d*x)/2)^5*((20*A*a)/3 + (116*C*a)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
85,1,166,117,5.073334,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(-A\,a-\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(5\,A\,a+\frac{49\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-7\,A\,a-\frac{31\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + (13*C*a)/4) - tan(c/2 + (d*x)/2)^7*(A*a + (3*C*a)/4) - tan(c/2 + (d*x)/2)^3*(7*A*a + (31*C*a)/12) + tan(c/2 + (d*x)/2)^5*(5*A*a + (49*C*a)/12))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(4*A + 3*C))/(4*d)","B"
86,1,129,86,4.419055,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x),x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,A+C\right)}{d}-\frac{\left(2\,A\,a+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a-\frac{4\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(2*A + C))/d - (tan(c/2 + (d*x)/2)*(2*A*a + 3*C*a) + tan(c/2 + (d*x)/2)^5*(2*A*a + C*a) - tan(c/2 + (d*x)/2)^3*(4*A*a + (4*C*a)/3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
87,1,128,58,2.627362,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(2*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*sin(c + d*x))/(d*cos(c + d*x)) + (C*a*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
88,1,91,42,2.683973,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(A*a*sin(c + d*x))/d + (2*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*sin(c + d*x))/(d*cos(c + d*x))","B"
89,1,115,58,2.751934,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*a*sin(c + d*x))/d + (A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(2*c + 2*d*x))/(4*d)","B"
90,1,67,77,2.569917,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{A\,a\,x}{2}+C\,a\,x+\frac{3\,A\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(A*a*x)/2 + C*a*x + (3*A*a*sin(c + d*x))/(4*d) + (C*a*sin(c + d*x))/d + (A*a*sin(2*c + 2*d*x))/(4*d) + (A*a*sin(3*c + 3*d*x))/(12*d)","B"
91,1,184,95,5.169038,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{\left(\frac{3\,A\,a}{4}+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{49\,A\,a}{12}+5\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{31\,A\,a}{12}+7\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,C\right)}{4\,\left(\frac{3\,A\,a}{4}+C\,a\right)}\right)\,\left(3\,A+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*C*a) + tan(c/2 + (d*x)/2)^7*((3*A*a)/4 + C*a) + tan(c/2 + (d*x)/2)^3*((31*A*a)/12 + 7*C*a) + tan(c/2 + (d*x)/2)^5*((49*A*a)/12 + 5*C*a))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(3*A + 4*C))/(4*((3*A*a)/4 + C*a)))*(3*A + 4*C))/(4*d)","B"
92,1,218,131,5.211310,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{\left(\frac{3\,A\,a}{4}+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{13\,A\,a}{6}+\frac{10\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{19\,A\,a}{6}+\frac{22\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,C\right)}{4\,\left(\frac{3\,A\,a}{4}+C\,a\right)}\right)\,\left(3\,A+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*C*a) + tan(c/2 + (d*x)/2)^9*((3*A*a)/4 + C*a) + tan(c/2 + (d*x)/2)^7*((13*A*a)/6 + (10*C*a)/3) + tan(c/2 + (d*x)/2)^3*((19*A*a)/6 + (22*C*a)/3) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*C*a)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(3*A + 4*C))/(4*((3*A*a)/4 + C*a)))*(3*A + 4*C))/(4*d)","B"
93,1,222,172,5.200322,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{3\,C}{4}\right)}{d}-\frac{\left(2\,A\,a^2+\frac{3\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{28\,A\,a^2}{3}-7\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{56\,A\,a^2}{3}+\frac{72\,C\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{52\,A\,a^2}{3}-9\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A\,a^2+\frac{13\,C\,a^2}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a^2*atanh(tan(c/2 + (d*x)/2))*(A + (3*C)/4))/d - (tan(c/2 + (d*x)/2)*(6*A*a^2 + (13*C*a^2)/2) + tan(c/2 + (d*x)/2)^9*(2*A*a^2 + (3*C*a^2)/2) - tan(c/2 + (d*x)/2)^7*((28*A*a^2)/3 + 7*C*a^2) - tan(c/2 + (d*x)/2)^3*((52*A*a^2)/3 + 9*C*a^2) + tan(c/2 + (d*x)/2)^5*((56*A*a^2)/3 + (72*C*a^2)/5))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
94,1,185,132,5.004463,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/cos(c + d*x),x)","\frac{\left(-3\,A\,a^2-\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(11\,A\,a^2+\frac{77\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-13\,A\,a^2-\frac{83\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(5\,A\,a^2+\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(12\,A+7\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(5*A*a^2 + (25*C*a^2)/4) - tan(c/2 + (d*x)/2)^7*(3*A*a^2 + (7*C*a^2)/4) + tan(c/2 + (d*x)/2)^5*(11*A*a^2 + (77*C*a^2)/12) - tan(c/2 + (d*x)/2)^3*(13*A*a^2 + (83*C*a^2)/12))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a^2*atanh(tan(c/2 + (d*x)/2))*(12*A + 7*C))/(4*d)","B"
95,1,184,96,2.578710,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{5\,C\,a^2\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (5*C*a^2*sin(c + d*x))/(3*d*cos(c + d*x)) + (C*a^2*sin(c + d*x))/(d*cos(c + d*x)^2) + (C*a^2*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
96,1,154,112,2.604655,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{4\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(A*a^2*sin(c + d*x))/d + (4*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^2*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
97,1,152,119,2.641910,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(2*A*a^2*sin(c + d*x))/d + (3*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
98,1,159,110,2.675121,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{7\,A\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(7*A*a^2*sin(c + d*x))/(4*d) + (C*a^2*sin(c + d*x))/d + (2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^2*sin(2*c + 2*d*x))/(2*d) + (A*a^2*sin(3*c + 3*d*x))/(12*d)","B"
99,1,117,136,2.655215,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{7\,A\,a^2\,x}{8}+\frac{3\,C\,a^2\,x}{2}+\frac{3\,A\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{A\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(7*A*a^2*x)/8 + (3*C*a^2*x)/2 + (3*A*a^2*sin(c + d*x))/(2*d) + (2*C*a^2*sin(c + d*x))/d + (A*a^2*sin(2*c + 2*d*x))/(2*d) + (A*a^2*sin(3*c + 3*d*x))/(6*d) + (A*a^2*sin(4*c + 4*d*x))/(32*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d)","B"
100,1,247,169,5.342348,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{\left(\frac{3\,A\,a^2}{2}+2\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(7\,A\,a^2+\frac{28\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{72\,A\,a^2}{5}+\frac{56\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(9\,A\,a^2+\frac{52\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a^2}{2}+6\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,C\right)}{2\,\left(\frac{3\,A\,a^2}{2}+2\,C\,a^2\right)}\right)\,\left(3\,A+4\,C\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a^2)/2 + 6*C*a^2) + tan(c/2 + (d*x)/2)^9*((3*A*a^2)/2 + 2*C*a^2) + tan(c/2 + (d*x)/2)^7*(7*A*a^2 + (28*C*a^2)/3) + tan(c/2 + (d*x)/2)^3*(9*A*a^2 + (52*C*a^2)/3) + tan(c/2 + (d*x)/2)^5*((72*A*a^2)/5 + (56*C*a^2)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(3*A + 4*C))/(2*((3*A*a^2)/2 + 2*C*a^2)))*(3*A + 4*C))/(2*d)","B"
101,1,285,194,5.367127,"\text{Not used}","int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{\left(\frac{11\,A\,a^2}{8}+\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{187\,A\,a^2}{24}+\frac{119\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{331\,A\,a^2}{20}+\frac{43\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{501\,A\,a^2}{20}+\frac{53\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{87\,A\,a^2}{8}+\frac{233\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{53\,A\,a^2}{8}+\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,A+14\,C\right)}{8\,\left(\frac{11\,A\,a^2}{8}+\frac{7\,C\,a^2}{4}\right)}\right)\,\left(11\,A+14\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((53*A*a^2)/8 + (25*C*a^2)/4) + tan(c/2 + (d*x)/2)^11*((11*A*a^2)/8 + (7*C*a^2)/4) + tan(c/2 + (d*x)/2)^3*((87*A*a^2)/8 + (233*C*a^2)/12) + tan(c/2 + (d*x)/2)^9*((187*A*a^2)/24 + (119*C*a^2)/12) + tan(c/2 + (d*x)/2)^7*((331*A*a^2)/20 + (43*C*a^2)/2) + tan(c/2 + (d*x)/2)^5*((501*A*a^2)/20 + (53*C*a^2)/2))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(11*A + 14*C))/(8*((11*A*a^2)/8 + (7*C*a^2)/4)))*(11*A + 14*C))/(8*d)","B"
102,1,262,197,5.280001,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{\left(-\frac{15\,A\,a^3}{4}-\frac{23\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{85\,A\,a^3}{4}+\frac{391\,C\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{99\,A\,a^3}{2}-\frac{759\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{125\,A\,a^3}{2}+\frac{969\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{171\,A\,a^3}{4}-\frac{211\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,A\,a^3}{4}+\frac{105\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(30\,A+23\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + (105*C*a^3)/8) - tan(c/2 + (d*x)/2)^11*((15*A*a^3)/4 + (23*C*a^3)/8) - tan(c/2 + (d*x)/2)^3*((171*A*a^3)/4 + (211*C*a^3)/8) + tan(c/2 + (d*x)/2)^9*((85*A*a^3)/4 + (391*C*a^3)/24) - tan(c/2 + (d*x)/2)^7*((99*A*a^3)/2 + (759*C*a^3)/20) + tan(c/2 + (d*x)/2)^5*((125*A*a^3)/2 + (969*C*a^3)/20))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atanh(tan(c/2 + (d*x)/2))*(30*A + 23*C))/(8*d)","B"
103,1,224,157,5.110738,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/cos(c + d*x),x)","\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(20\,A+13\,C\right)}{4\,d}-\frac{\left(5\,A\,a^3+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{70\,A\,a^3}{3}-\frac{91\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{128\,A\,a^3}{3}+\frac{416\,C\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{106\,A\,a^3}{3}-\frac{133\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A\,a^3+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh(tan(c/2 + (d*x)/2))*(20*A + 13*C))/(4*d) - (tan(c/2 + (d*x)/2)*(11*A*a^3 + (51*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*(5*A*a^3 + (13*C*a^3)/4) - tan(c/2 + (d*x)/2)^7*((70*A*a^3)/3 + (91*C*a^3)/6) - tan(c/2 + (d*x)/2)^3*((106*A*a^3)/3 + (133*C*a^3)/6) + tan(c/2 + (d*x)/2)^5*((128*A*a^3)/3 + (416*C*a^3)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
104,1,231,147,2.653923,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{2\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{15\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{15\,C\,a^3\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}","Not used",1,"(2*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (15*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (3*A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (3*C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (15*C*a^3*sin(c + d*x))/(8*d*cos(c + d*x)^2) + (C*a^3*sin(c + d*x))/(d*cos(c + d*x)^3) + (C*a^3*sin(c + d*x))/(4*d*cos(c + d*x)^4)","B"
105,1,199,145,2.666474,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{6\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{5\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{11\,C\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(A*a^3*sin(c + d*x))/d + (6*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (5*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (11*C*a^3*sin(c + d*x))/(3*d*cos(c + d*x)) + (3*C*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (C*a^3*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
106,1,207,162,2.744159,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{7\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(3*A*a^3*sin(c + d*x))/d + (7*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (A*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
107,1,189,156,2.717002,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{11\,A\,a^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{3\,A\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(11*A*a^3*sin(c + d*x))/(3*d) + (C*a^3*sin(c + d*x))/d + (5*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^3*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (3*A*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
108,1,195,169,2.852816,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{13\,A\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{15\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{7\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(13*A*a^3*sin(c + d*x))/(4*d) + (3*C*a^3*sin(c + d*x))/d + (15*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (7*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^3*sin(2*c + 2*d*x))/d + (A*a^3*sin(3*c + 3*d*x))/(4*d) + (A*a^3*sin(4*c + 4*d*x))/(32*d) + (C*a^3*sin(2*c + 2*d*x))/(4*d)","B"
109,1,247,161,5.316986,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{13\,A\,a^3}{4}+5\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{91\,A\,a^3}{6}+\frac{70\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,A\,a^3}{15}+\frac{128\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{133\,A\,a^3}{6}+\frac{106\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+11\,C\,a^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,A+20\,C\right)}{4\,\left(\frac{13\,A\,a^3}{4}+5\,C\,a^3\right)}\right)\,\left(13\,A+20\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + 11*C*a^3) + tan(c/2 + (d*x)/2)^9*((13*A*a^3)/4 + 5*C*a^3) + tan(c/2 + (d*x)/2)^7*((91*A*a^3)/6 + (70*C*a^3)/3) + tan(c/2 + (d*x)/2)^3*((133*A*a^3)/6 + (106*C*a^3)/3) + tan(c/2 + (d*x)/2)^5*((416*A*a^3)/15 + (128*C*a^3)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(13*A + 20*C))/(4*((13*A*a^3)/4 + 5*C*a^3)))*(13*A + 20*C))/(4*d)","B"
110,1,285,216,5.381890,"\text{Not used}","int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{23\,A\,a^3}{8}+\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{391\,A\,a^3}{24}+\frac{85\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{759\,A\,a^3}{20}+\frac{99\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{969\,A\,a^3}{20}+\frac{125\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{211\,A\,a^3}{8}+\frac{171\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{105\,A\,a^3}{8}+\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,A+30\,C\right)}{8\,\left(\frac{23\,A\,a^3}{8}+\frac{15\,C\,a^3}{4}\right)}\right)\,\left(23\,A+30\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((105*A*a^3)/8 + (49*C*a^3)/4) + tan(c/2 + (d*x)/2)^11*((23*A*a^3)/8 + (15*C*a^3)/4) + tan(c/2 + (d*x)/2)^3*((211*A*a^3)/8 + (171*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((391*A*a^3)/24 + (85*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((759*A*a^3)/20 + (99*C*a^3)/2) + tan(c/2 + (d*x)/2)^5*((969*A*a^3)/20 + (125*C*a^3)/2))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(23*A + 30*C))/(8*((23*A*a^3)/8 + (15*C*a^3)/4)))*(23*A + 30*C))/(8*d)","B"
111,1,301,228,5.408639,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4)/cos(c + d*x)^2,x)","\frac{a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(14\,A+11\,C\right)}{2\,d}-\frac{\left(7\,A\,a^4+\frac{11\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(-\frac{140\,A\,a^4}{3}-\frac{110\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1981\,A\,a^4}{15}+\frac{3113\,C\,a^4}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{1024\,A\,a^4}{5}-\frac{5632\,C\,a^4}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{2851\,A\,a^4}{15}+\frac{1501\,C\,a^4}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{308\,A\,a^4}{3}-70\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{53\,C\,a^4}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^4*atanh(tan(c/2 + (d*x)/2))*(14*A + 11*C))/(2*d) - (tan(c/2 + (d*x)/2)*(25*A*a^4 + (53*C*a^4)/2) + tan(c/2 + (d*x)/2)^13*(7*A*a^4 + (11*C*a^4)/2) - tan(c/2 + (d*x)/2)^11*((140*A*a^4)/3 + (110*C*a^4)/3) - tan(c/2 + (d*x)/2)^3*((308*A*a^4)/3 + 70*C*a^4) + tan(c/2 + (d*x)/2)^5*((2851*A*a^4)/15 + (1501*C*a^4)/10) + tan(c/2 + (d*x)/2)^9*((1981*A*a^4)/15 + (3113*C*a^4)/30) - tan(c/2 + (d*x)/2)^7*((1024*A*a^4)/5 + (5632*C*a^4)/35))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
112,1,262,188,5.319629,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4)/cos(c + d*x),x)","\frac{\left(-\frac{35\,A\,a^4}{4}-\frac{49\,C\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{595\,A\,a^4}{12}+\frac{833\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{231\,A\,a^4}{2}-\frac{1617\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{281\,A\,a^4}{2}+\frac{1967\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{1069\,A\,a^4}{12}-\frac{1471\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{93\,A\,a^4}{4}+\frac{207\,C\,a^4}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{7\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(10\,A+7\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + (207*C*a^4)/8) - tan(c/2 + (d*x)/2)^11*((35*A*a^4)/4 + (49*C*a^4)/8) + tan(c/2 + (d*x)/2)^9*((595*A*a^4)/12 + (833*C*a^4)/24) - tan(c/2 + (d*x)/2)^7*((231*A*a^4)/2 + (1617*C*a^4)/20) + tan(c/2 + (d*x)/2)^5*((281*A*a^4)/2 + (1967*C*a^4)/20) - tan(c/2 + (d*x)/2)^3*((1069*A*a^4)/12 + (1471*C*a^4)/24))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (7*a^4*atanh(tan(c/2 + (d*x)/2))*(10*A + 7*C))/(8*d)","B"
113,1,277,177,2.809650,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{2\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{12\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{83\,C\,a^4\,\sin\left(c+d\,x\right)}{15\,d\,\cos\left(c+d\,x\right)}+\frac{7\,C\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{34\,C\,a^4\,\sin\left(c+d\,x\right)}{15\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^4}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{5\,d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"(2*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (20*A*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (2*A*a^4*sin(c + d*x))/(d*cos(c + d*x)^2) + (A*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (83*C*a^4*sin(c + d*x))/(15*d*cos(c + d*x)) + (7*C*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (34*C*a^4*sin(c + d*x))/(15*d*cos(c + d*x)^3) + (C*a^4*sin(c + d*x))/(d*cos(c + d*x)^4) + (C*a^4*sin(c + d*x))/(5*d*cos(c + d*x)^5)","B"
114,1,246,181,2.791140,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{8\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{13\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{35\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{20\,C\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{27\,C\,a^4\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{4\,C\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}","Not used",1,"(A*a^4*sin(c + d*x))/d + (8*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (35*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (4*A*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (20*C*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (27*C*a^4*sin(c + d*x))/(8*d*cos(c + d*x)^2) + (4*C*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (C*a^4*sin(c + d*x))/(4*d*cos(c + d*x)^4)","B"
115,1,252,192,2.847926,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{13\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{8\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{12\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{20\,C\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(4*A*a^4*sin(c + d*x))/d + (13*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (20*C*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (2*C*a^4*sin(c + d*x))/(d*cos(c + d*x)^2) + (C*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (A*a^4*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
116,1,244,198,2.895791,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{12\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{8\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{13\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{4\,C\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{2\,A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(20*A*a^4*sin(c + d*x))/(3*d) + (C*a^4*sin(c + d*x))/d + (12*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (4*C*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (2*A*a^4*cos(c + d*x)*sin(c + d*x))/d","B"
117,1,234,200,2.815084,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d}+\frac{4\,C\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{35\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{13\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{8\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,A\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{A\,a^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{27\,A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{C\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(20*A*a^4*sin(c + d*x))/(3*d) + (4*C*a^4*sin(c + d*x))/d + (35*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (13*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*A*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (A*a^4*cos(c + d*x)^3*sin(c + d*x))/(4*d) + (C*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (27*A*a^4*cos(c + d*x)*sin(c + d*x))/(8*d) + (C*a^4*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
118,1,202,207,3.311349,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{7\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+12\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{29\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48}+\frac{A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{80}+C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{12}+\frac{49\,A\,a^4\,\sin\left(c+d\,x\right)}{8}+\frac{27\,C\,a^4\,\sin\left(c+d\,x\right)}{4}}{d}","Not used",1,"(7*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 12*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*A*a^4*sin(2*c + 2*d*x) + (29*A*a^4*sin(3*c + 3*d*x))/48 + (A*a^4*sin(4*c + 4*d*x))/8 + (A*a^4*sin(5*c + 5*d*x))/80 + C*a^4*sin(2*c + 2*d*x) + (C*a^4*sin(3*c + 3*d*x))/12 + (49*A*a^4*sin(c + d*x))/8 + (27*C*a^4*sin(c + d*x))/4)/d","B"
119,1,286,192,5.403795,"\text{Not used}","int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{\left(\frac{49\,A\,a^4}{8}+\frac{35\,C\,a^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{833\,A\,a^4}{24}+\frac{595\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{1617\,A\,a^4}{20}+\frac{231\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1967\,A\,a^4}{20}+\frac{281\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{1471\,A\,a^4}{24}+\frac{1069\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+\frac{93\,C\,a^4}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{7\,a^4\,\mathrm{atan}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,A+10\,C\right)}{8\,\left(\frac{49\,A\,a^4}{8}+\frac{35\,C\,a^4}{4}\right)}\right)\,\left(7\,A+10\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + (93*C*a^4)/4) + tan(c/2 + (d*x)/2)^11*((49*A*a^4)/8 + (35*C*a^4)/4) + tan(c/2 + (d*x)/2)^9*((833*A*a^4)/24 + (595*C*a^4)/12) + tan(c/2 + (d*x)/2)^7*((1617*A*a^4)/20 + (231*C*a^4)/2) + tan(c/2 + (d*x)/2)^5*((1967*A*a^4)/20 + (281*C*a^4)/2) + tan(c/2 + (d*x)/2)^3*((1471*A*a^4)/24 + (1069*C*a^4)/12))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (7*a^4*atan((7*a^4*tan(c/2 + (d*x)/2)*(7*A + 10*C))/(8*((49*A*a^4)/8 + (35*C*a^4)/4)))*(7*A + 10*C))/(8*d)","B"
120,1,323,254,4.777477,"\text{Not used}","int(cos(c + d*x)^7*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^4,x)","\frac{\left(\frac{11\,A\,a^4}{2}+7\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{110\,A\,a^4}{3}+\frac{140\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3113\,A\,a^4}{30}+\frac{1981\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{5632\,A\,a^4}{35}+\frac{1024\,C\,a^4}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1501\,A\,a^4}{10}+\frac{2851\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(70\,A\,a^4+\frac{308\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{53\,A\,a^4}{2}+25\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,A+14\,C\right)}{2\,\left(\frac{11\,A\,a^4}{2}+7\,C\,a^4\right)}\right)\,\left(11\,A+14\,C\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((53*A*a^4)/2 + 25*C*a^4) + tan(c/2 + (d*x)/2)^13*((11*A*a^4)/2 + 7*C*a^4) + tan(c/2 + (d*x)/2)^11*((110*A*a^4)/3 + (140*C*a^4)/3) + tan(c/2 + (d*x)/2)^3*(70*A*a^4 + (308*C*a^4)/3) + tan(c/2 + (d*x)/2)^5*((1501*A*a^4)/10 + (2851*C*a^4)/15) + tan(c/2 + (d*x)/2)^9*((3113*A*a^4)/30 + (1981*C*a^4)/15) + tan(c/2 + (d*x)/2)^7*((5632*A*a^4)/35 + (1024*C*a^4)/5))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(11*A + 14*C))/(2*((11*A*a^4)/2 + 7*C*a^4)))*(11*A + 14*C))/(2*d)","B"
121,1,184,165,3.628151,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))),x)","\frac{\left(3\,A+\frac{25\,C}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-7\,A-\frac{115\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(5\,A+\frac{109\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-A-\frac{7\,C}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}+\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+5\,C\right)}{4\,a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(3*A + (25*C)/4) + tan(c/2 + (d*x)/2)^3*(5*A + (109*C)/12) - tan(c/2 + (d*x)/2)^5*(7*A + (115*C)/12) - tan(c/2 + (d*x)/2)*(A + (7*C)/4))/(d*(a - 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 - 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8)) - (tan(c/2 + (d*x)/2)*(A + C))/(a*d) + (3*atanh(tan(c/2 + (d*x)/2))*(4*A + 5*C))/(4*a*d)","B"
122,1,150,133,2.987916,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))),x)","\frac{\left(2\,A+5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A-\frac{16\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A+3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{3\,C}{2}\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(2*A + 5*C) - tan(c/2 + (d*x)/2)^3*(4*A + (16*C)/3) + tan(c/2 + (d*x)/2)*(2*A + 3*C))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6)) - (2*atanh(tan(c/2 + (d*x)/2))*(A + (3*C)/2))/(a*d) + (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
123,1,106,107,2.672277,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{3\,C}{2}\right)}{a\,d}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A + (3*C)/2))/(a*d) - (C*tan(c/2 + (d*x)/2) - 3*C*tan(c/2 + (d*x)/2)^3)/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
124,1,72,57,2.604814,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))),x)","\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(2*C*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) - (2*C*atanh(tan(c/2 + (d*x)/2)))/(a*d) + (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
125,1,101,49,2.735321,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x)),x)","\frac{2\,A\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(2*A*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) - (A*sin(c/2 + (d*x)/2) + C*sin(c/2 + (d*x)/2))/(a*d*cos(c/2 + (d*x)/2))","B"
126,1,59,52,2.597677,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{A\,x}{a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(2*A*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - (A*x)/a + (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
127,1,83,96,2.607374,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{3\,A\,x}{2\,a}+\frac{C\,x}{a}-\frac{A\,\sin\left(c+d\,x\right)}{a\,d}+\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(3*A*x)/(2*a) + (C*x)/a - (A*sin(c + d*x))/(a*d) + (A*sin(2*c + 2*d*x))/(4*a*d) - (A*tan(c/2 + (d*x)/2))/(a*d) - (C*tan(c/2 + (d*x)/2))/(a*d)","B"
128,1,114,124,2.661216,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{7\,A\,\sin\left(c+d\,x\right)}{4\,a\,d}-\frac{C\,x}{a}-\frac{3\,A\,x}{2\,a}+\frac{C\,\sin\left(c+d\,x\right)}{a\,d}-\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}+\frac{A\,\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(7*A*sin(c + d*x))/(4*a*d) - (C*x)/a - (3*A*x)/(2*a) + (C*sin(c + d*x))/(a*d) - (A*sin(2*c + 2*d*x))/(4*a*d) + (A*sin(3*c + 3*d*x))/(12*a*d) + (A*tan(c/2 + (d*x)/2))/(a*d) + (C*tan(c/2 + (d*x)/2))/(a*d)","B"
129,1,153,156,2.748556,"\text{Not used}","int((cos(c + d*x)^4*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{15\,A\,x}{8\,a}+\frac{3\,C\,x}{2\,a}-\frac{7\,A\,\sin\left(c+d\,x\right)}{4\,a\,d}-\frac{C\,\sin\left(c+d\,x\right)}{a\,d}+\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{2\,a\,d}-\frac{A\,\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{A\,\sin\left(4\,c+4\,d\,x\right)}{32\,a\,d}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}+\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(15*A*x)/(8*a) + (3*C*x)/(2*a) - (7*A*sin(c + d*x))/(4*a*d) - (C*sin(c + d*x))/(a*d) + (A*sin(2*c + 2*d*x))/(2*a*d) - (A*sin(3*c + 3*d*x))/(12*a*d) + (A*sin(4*c + 4*d*x))/(32*a*d) - (A*tan(c/2 + (d*x)/2))/(a*d) + (C*sin(2*c + 2*d*x))/(4*a*d) - (C*tan(c/2 + (d*x)/2))/(a*d)","B"
130,1,197,172,2.744207,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(A+C\right)}{a^2}+\frac{A+5\,C}{2\,a^2}\right)}{d}-\frac{\left(2\,A+10\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A-\frac{40\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A+6\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,A+5\,C\right)}{a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((2*(A + C))/a^2 + (A + 5*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^5*(2*A + 10*C) - tan(c/2 + (d*x)/2)^3*(4*A + (40*C)/3) + tan(c/2 + (d*x)/2)*(2*A + 6*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 - 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 - a^2)) - (2*atanh(tan(c/2 + (d*x)/2))*(2*A + 5*C))/(a^2*d) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
131,1,144,150,2.693265,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^2),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{7\,C}{2}\right)}{a^2\,d}-\frac{3\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^2}+\frac{2\,C}{a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A + (7*C)/2))/(a^2*d) - (3*C*tan(c/2 + (d*x)/2) - 5*C*tan(c/2 + (d*x)/2)^3)/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^2) + (2*C)/a^2))/d - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
132,1,111,99,2.696320,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{a^2}-\frac{A-3\,C}{2\,a^2}\right)}{d}-\frac{4\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A + C)/a^2 - (A - 3*C)/(2*a^2)))/d - (4*C*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (2*C*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
133,1,77,75,2.624096,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^2),x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{2\,a^2}-\frac{2\,A-2\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)*((A + C)/(2*a^2) - (2*A - 2*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
134,1,64,68,2.575988,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^2,x)","\frac{3\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,A\,d\,x}{6\,a^2\,d}","Not used",1,"(3*C*tan(c/2 + (d*x)/2) - 9*A*tan(c/2 + (d*x)/2) + A*tan(c/2 + (d*x)/2)^3 + C*tan(c/2 + (d*x)/2)^3 + 6*A*d*x)/(6*a^2*d)","B"
135,1,99,82,2.647372,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{a^2}+\frac{3\,A-C}{2\,a^2}\right)}{d}-\frac{2\,A\,x}{a^2}+\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A + C)/a^2 + (3*A - C)/(2*a^2)))/d - (2*A*x)/a^2 + (2*A*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
136,1,134,137,2.662231,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{x\,\left(7\,A+2\,C\right)}{2\,a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^2}+\frac{2\,A}{a^2}\right)}{d}-\frac{5\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(x*(7*A + 2*C))/(2*a^2) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^2) + (2*A)/a^2))/d - (3*A*tan(c/2 + (d*x)/2) + 5*A*tan(c/2 + (d*x)/2)^3)/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2)) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
137,1,181,163,2.682959,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{\left(10\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{40\,A}{3}+4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{x\,\left(5\,A+2\,C\right)}{a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(A+C\right)}{a^2}+\frac{5\,A+C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(10*A + 2*C) + tan(c/2 + (d*x)/2)^3*((40*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(6*A + 2*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2)) - (x*(5*A + 2*C))/a^2 + (tan(c/2 + (d*x)/2)*((2*(A + C))/a^2 + (5*A + C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
138,1,195,198,2.652249,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^3),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{13\,C}{2}\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^3}+\frac{3\,\left(A+5\,C\right)}{4\,a^3}-\frac{2\,A-10\,C}{4\,a^3}\right)}{d}-\frac{5\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-7\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^3}+\frac{A+5\,C}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A + (13*C)/2))/(a^3*d) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^3) + (3*(A + 5*C))/(4*a^3) - (2*A - 10*C)/(4*a^3)))/d - (5*C*tan(c/2 + (d*x)/2) - 7*C*tan(c/2 + (d*x)/2)^3)/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^3) + (A + 5*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
139,1,150,145,2.637411,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{6\,a^3}+\frac{C}{3\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{4\,a^3}+\frac{2\,C}{a^3}-\frac{2\,A-6\,C}{4\,a^3}\right)}{d}-\frac{6\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A + C)/(6*a^3) + C/(3*a^3)))/d + (tan(c/2 + (d*x)/2)*((3*(A + C))/(4*a^3) + (2*C)/a^3 - (2*A - 6*C)/(4*a^3)))/d - (6*C*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (2*C*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
140,1,110,123,2.641530,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^3),x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{4\,a^3}-\frac{A-3\,C}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{12\,a^3}-\frac{A-3\,C}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (tan(c/2 + (d*x)/2)*((A + C)/(4*a^3) - (A - 3*C)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((A + C)/(12*a^3) - (A - 3*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
141,1,69,104,2.573099,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{4\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-2\,C\right)}{12\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A + C))/(4*a^3*d) - (tan(c/2 + (d*x)/2)^3*(2*A - 2*C))/(12*a^3*d) + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
142,1,117,106,2.815863,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^3,x)","\frac{A\,x}{a^3}-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{7\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)+\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{A\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(A*x)/a^3 - (cos(c/2 + (d*x)/2)^4*((7*A*sin(c/2 + (d*x)/2))/4 - (C*sin(c/2 + (d*x)/2))/4) + (A*sin(c/2 + (d*x)/2)^5)/20 + (C*sin(c/2 + (d*x)/2)^5)/20 - (A*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^3)/3)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
143,1,153,120,2.744009,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{24\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{7\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{3\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}-\frac{4\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{20}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-\frac{3\,A\,x}{a^3}+\frac{2\,A\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}","Not used",1,"((A*sin(c/2 + (d*x)/2))/20 + (C*sin(c/2 + (d*x)/2))/20 - cos(c/2 + (d*x)/2)^2*((3*A*sin(c/2 + (d*x)/2))/5 + (4*C*sin(c/2 + (d*x)/2))/15) + cos(c/2 + (d*x)/2)^4*((24*A*sin(c/2 + (d*x)/2))/5 + (7*C*sin(c/2 + (d*x)/2))/15))/(a^3*d*cos(c/2 + (d*x)/2)^5) - (3*A*x)/a^3 + (2*A*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^3*d)","B"
144,1,184,183,2.687021,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^3}+\frac{5\,A+C}{12\,a^3}\right)}{d}+\frac{x\,\left(13\,A+2\,C\right)}{2\,a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^3}+\frac{3\,\left(5\,A+C\right)}{4\,a^3}+\frac{10\,A-2\,C}{4\,a^3}\right)}{d}-\frac{7\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^3) + (5*A + C)/(12*a^3)))/d + (x*(13*A + 2*C))/(2*a^3) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^3) + (3*(5*A + C))/(4*a^3) + (10*A - 2*C)/(4*a^3)))/d - (5*A*tan(c/2 + (d*x)/2) + 7*A*tan(c/2 + (d*x)/2)^3)/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3)) - (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
145,1,231,216,2.682456,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{\left(17\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{76\,A}{3}+4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{x\,\left(23\,A+6\,C\right)}{2\,a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{3\,a^3}+\frac{6\,A+2\,C}{12\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{2\,a^3}+\frac{6\,A+2\,C}{a^3}+\frac{15\,A-C}{4\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(17*A + 2*C) + tan(c/2 + (d*x)/2)^3*((76*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(11*A + 2*C))/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 + 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 + a^3)) - (x*(23*A + 6*C))/(2*a^3) - (tan(c/2 + (d*x)/2)^3*((A + C)/(3*a^3) + (6*A + 2*C)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((5*(A + C))/(2*a^3) + (6*A + 2*C)/a^3 + (15*A - C)/(4*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
146,1,256,232,2.643498,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a/cos(c + d*x))^4),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{21\,C}{2}\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,\left(A+C\right)}{40\,a^4}+\frac{2\,A+6\,C}{40\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^4}-\frac{A-15\,C}{24\,a^4}+\frac{2\,A+6\,C}{8\,a^4}\right)}{d}-\frac{7\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{4\,a^4}-\frac{3\,\left(A-15\,C\right)}{8\,a^4}+\frac{3\,\left(2\,A+6\,C\right)}{4\,a^4}-\frac{4\,A-20\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A + (21*C)/2))/(a^4*d) - (tan(c/2 + (d*x)/2)^5*((3*(A + C))/(40*a^4) + (2*A + 6*C)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^4) - (A - 15*C)/(24*a^4) + (2*A + 6*C)/(8*a^4)))/d - (7*C*tan(c/2 + (d*x)/2) - 9*C*tan(c/2 + (d*x)/2)^3)/(d*(a^4*tan(c/2 + (d*x)/2)^4 - 2*a^4*tan(c/2 + (d*x)/2)^2 + a^4)) - (tan(c/2 + (d*x)/2)*((5*(A + C))/(4*a^4) - (3*(A - 15*C))/(8*a^4) + (3*(2*A + 6*C))/(4*a^4) - (4*A - 20*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
147,1,204,183,2.558653,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A+C}{20\,a^4}+\frac{A+5\,C}{40\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{2\,a^4}+\frac{3\,\left(A+5\,C\right)}{8\,a^4}-\frac{3\,\left(2\,A-10\,C\right)}{8\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{8\,a^4}+\frac{A+5\,C}{12\,a^4}-\frac{2\,A-10\,C}{24\,a^4}\right)}{d}-\frac{8\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((A + C)/(20*a^4) + (A + 5*C)/(40*a^4)))/d + (tan(c/2 + (d*x)/2)*((A + C)/(2*a^4) + (3*(A + 5*C))/(8*a^4) - (3*(2*A - 10*C))/(8*a^4)))/d + (tan(c/2 + (d*x)/2)^3*((A + C)/(8*a^4) + (A + 5*C)/(12*a^4) - (2*A - 10*C)/(24*a^4)))/d - (8*C*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (2*C*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4)) + (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
148,1,156,161,2.567087,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^4),x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{8\,a^4}+\frac{C}{a^4}-\frac{2\,A-6\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{24\,a^4}+\frac{C}{6\,a^4}-\frac{2\,A-6\,C}{24\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A+C}{40\,a^4}+\frac{C}{10\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (tan(c/2 + (d*x)/2)*((A + C)/(8*a^4) + C/a^4 - (2*A - 6*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((A + C)/(24*a^4) + C/(6*a^4) - (2*A - 6*C)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((A + C)/(40*a^4) + C/(10*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
149,1,83,138,2.584503,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-3\,C\right)}{24\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-3\,C\right)}{40\,a^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{8\,a^4}}{d}","Not used",1,"((tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4) - (tan(c/2 + (d*x)/2)^3*(A - 3*C))/(24*a^4) - (tan(c/2 + (d*x)/2)^5*(A - 3*C))/(40*a^4) + (tan(c/2 + (d*x)/2)*(A + C))/(8*a^4))/d","B"
150,1,88,142,2.556874,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^4),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{8\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A-C\right)}{24\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A-C\right)}{40\,a^4}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4) - (tan(c/2 + (d*x)/2)*(A + C))/(8*a^4) + (tan(c/2 + (d*x)/2)^3*(3*A - C))/(24*a^4) - (tan(c/2 + (d*x)/2)^5*(3*A - C))/(40*a^4))/d","B"
151,1,163,136,2.638489,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^4,x)","\frac{A\,x}{a^4}+\frac{\left(\frac{13\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-\frac{52\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{16\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}+\frac{13\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{210}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{5\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{28}-\frac{11\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{140}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(A*x)/a^4 + ((A*sin(c/2 + (d*x)/2))/56 + (C*sin(c/2 + (d*x)/2))/56 - cos(c/2 + (d*x)/2)^2*((5*A*sin(c/2 + (d*x)/2))/28 + (11*C*sin(c/2 + (d*x)/2))/140) - cos(c/2 + (d*x)/2)^6*((52*A*sin(c/2 + (d*x)/2))/21 - (13*C*sin(c/2 + (d*x)/2))/105) + cos(c/2 + (d*x)/2)^4*((16*A*sin(c/2 + (d*x)/2))/21 + (13*C*sin(c/2 + (d*x)/2))/210))/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
152,1,192,152,2.754643,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\frac{2\,A\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4\,d}-\frac{\left(-\frac{764\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-\frac{12\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{143\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}+\frac{23\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{8\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}-\frac{9\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}-\frac{4\,A\,x}{a^4}","Not used",1,"(2*A*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^4*d) - ((A*sin(c/2 + (d*x)/2))/56 + (C*sin(c/2 + (d*x)/2))/56 - cos(c/2 + (d*x)/2)^2*((8*A*sin(c/2 + (d*x)/2))/35 + (9*C*sin(c/2 + (d*x)/2))/70) + cos(c/2 + (d*x)/2)^4*((143*A*sin(c/2 + (d*x)/2))/105 + (23*C*sin(c/2 + (d*x)/2))/70) - cos(c/2 + (d*x)/2)^6*((764*A*sin(c/2 + (d*x)/2))/105 + (12*C*sin(c/2 + (d*x)/2))/35))/(a^4*d*cos(c/2 + (d*x)/2)^7) - (4*A*x)/a^4","B"
153,1,249,215,2.701111,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\frac{x\,\left(21\,A+2\,C\right)}{2\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^4}+\frac{6\,A+2\,C}{8\,a^4}+\frac{15\,A-C}{24\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,\left(A+C\right)}{40\,a^4}+\frac{6\,A+2\,C}{40\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{4\,a^4}+\frac{3\,\left(6\,A+2\,C\right)}{4\,a^4}+\frac{3\,\left(15\,A-C\right)}{8\,a^4}+\frac{20\,A-4\,C}{8\,a^4}\right)}{d}-\frac{9\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(x*(21*A + 2*C))/(2*a^4) + (tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^4) + (6*A + 2*C)/(8*a^4) + (15*A - C)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((3*(A + C))/(40*a^4) + (6*A + 2*C)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)*((5*(A + C))/(4*a^4) + (3*(6*A + 2*C))/(4*a^4) + (3*(15*A - C))/(8*a^4) + (20*A - 4*C)/(8*a^4)))/d - (7*A*tan(c/2 + (d*x)/2) + 9*A*tan(c/2 + (d*x)/2)^3)/(d*(2*a^4*tan(c/2 + (d*x)/2)^2 + a^4*tan(c/2 + (d*x)/2)^4 + a^4)) + (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
154,1,198,248,2.690688,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{209\,A}{8}+\frac{49\,C}{8}\right)}{a^4\,d}-\frac{22\,A\,d\,x+4\,C\,d\,x}{a^4\,d}+\frac{\left(26\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{124\,A}{3}+4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(18\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{11\,A}{40}+\frac{7\,C}{40}\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{A}{56}+\frac{C}{56}\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{59\,A}{24}+\frac{23\,C}{24}\right)}{a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((209*A)/8 + (49*C)/8))/(a^4*d) - (22*A*d*x + 4*C*d*x)/(a^4*d) + (tan(c/2 + (d*x)/2)^5*(26*A + 2*C) + tan(c/2 + (d*x)/2)^3*((124*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(18*A + 2*C))/(a^4*d*(tan(c/2 + (d*x)/2)^2 + 1)^3) + (tan(c/2 + (d*x)/2)^5*((11*A)/40 + (7*C)/40))/(a^4*d) - (tan(c/2 + (d*x)/2)^7*(A/56 + C/56))/(a^4*d) - (tan(c/2 + (d*x)/2)^3*((59*A)/24 + (23*C)/24))/(a^4*d)","B"
155,1,636,223,12.199588,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,16{}\mathrm{i}}{9\,d}+\frac{C\,256{}\mathrm{i}}{33\,d}+\frac{\left(176\,A+704\,C\right)\,1{}\mathrm{i}}{99\,d}\right)-\frac{A\,16{}\mathrm{i}}{9\,d}+\frac{C\,64{}\mathrm{i}}{9\,d}+\frac{\left(176\,A+704\,C\right)\,1{}\mathrm{i}}{99\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,32{}\mathrm{i}}{11\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,32{}\mathrm{i}}{11\,d}-\frac{\left(32\,A+64\,C\right)\,1{}\mathrm{i}}{11\,d}\right)-\frac{\left(32\,A+64\,C\right)\,1{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}+\frac{\left(\frac{A\,16{}\mathrm{i}}{5\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,16{}\mathrm{i}}{5\,d}+\frac{\left(528\,A-320\,C\right)\,1{}\mathrm{i}}{1155\,d}\right)\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,16{}\mathrm{i}}{7\,d}-\frac{C\,7232{}\mathrm{i}}{693\,d}\right)+\frac{A\,16{}\mathrm{i}}{7\,d}-\frac{C\,64{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(3168\,A+2560\,C\right)\,1{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(1584\,A+1280\,C\right)\,1{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"(((A*16i)/(5*d) + exp(c*1i + d*x*1i)*((A*16i)/(5*d) + ((528*A - 320*C)*1i)/(1155*d)))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*32i)/(11*d) + exp(c*1i + d*x*1i)*((A*32i)/(11*d) - ((32*A + 64*C)*1i)/(11*d)) - ((32*A + 64*C)*1i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*256i)/(33*d) - (A*16i)/(9*d) + ((176*A + 704*C)*1i)/(99*d)) - (A*16i)/(9*d) + (C*64i)/(9*d) + ((176*A + 704*C)*1i)/(99*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*16i)/(7*d) - (C*7232i)/(693*d)) + (A*16i)/(7*d) - (C*64i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(3168*A + 2560*C)*1i)/(3465*d*(exp(c*1i + d*x*1i) + 1)) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1584*A + 1280*C)*1i)/(3465*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
156,1,535,180,11.227329,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,8{}\mathrm{i}}{7\,d}+\frac{C\,32{}\mathrm{i}}{63\,d}+\frac{\left(72\,A+288\,C\right)\,1{}\mathrm{i}}{63\,d}\right)+\frac{A\,8{}\mathrm{i}}{7\,d}-\frac{C\,32{}\mathrm{i}}{7\,d}-\frac{\left(72\,A+288\,C\right)\,1{}\mathrm{i}}{63\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{A\,16{}\mathrm{i}}{9\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,16{}\mathrm{i}}{9\,d}-\frac{\left(16\,A+32\,C\right)\,1{}\mathrm{i}}{9\,d}\right)+\frac{\left(16\,A+32\,C\right)\,1{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\left(\frac{A\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(168\,A+128\,C\right)\,1{}\mathrm{i}}{315\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,8{}\mathrm{i}}{5\,d}-\frac{C\,32{}\mathrm{i}}{105\,d}\right)-\frac{A\,8{}\mathrm{i}}{5\,d}+\frac{C\,32{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(336\,A+256\,C\right)\,1{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*32i)/(63*d) - (A*8i)/(7*d) + ((72*A + 288*C)*1i)/(63*d)) + (A*8i)/(7*d) - (C*32i)/(7*d) - ((72*A + 288*C)*1i)/(63*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*16i)/(9*d) - ((16*A + 32*C)*1i)/(9*d)) - (A*16i)/(9*d) + ((16*A + 32*C)*1i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + (((A*8i)/(3*d) - (exp(c*1i + d*x*1i)*(168*A + 128*C)*1i)/(315*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*8i)/(5*d) - (C*32i)/(105*d)) - (A*8i)/(5*d) + (C*32i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(336*A + 256*C)*1i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
157,1,423,137,6.213311,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\frac{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,4{}\mathrm{i}}{3\,d}-\frac{C\,16{}\mathrm{i}}{35\,d}\right)+\frac{A\,4{}\mathrm{i}}{3\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,8{}\mathrm{i}}{7\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,8{}\mathrm{i}}{7\,d}-\frac{\left(8\,A+16\,C\right)\,1{}\mathrm{i}}{7\,d}\right)-\frac{\left(8\,A+16\,C\right)\,1{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,4{}\mathrm{i}}{5\,d}+\frac{C\,16{}\mathrm{i}}{35\,d}+\frac{\left(28\,A+112\,C\right)\,1{}\mathrm{i}}{35\,d}\right)-\frac{A\,4{}\mathrm{i}}{5\,d}+\frac{\left(28\,A+112\,C\right)\,1{}\mathrm{i}}{35\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(140\,A+96\,C\right)\,1{}\mathrm{i}}{105\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((exp(c*1i + d*x*1i)*((A*4i)/(3*d) - (C*16i)/(35*d)) + (A*4i)/(3*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*8i)/(7*d) + exp(c*1i + d*x*1i)*((A*8i)/(7*d) - ((8*A + 16*C)*1i)/(7*d)) - ((8*A + 16*C)*1i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*16i)/(35*d) - (A*4i)/(5*d) + ((28*A + 112*C)*1i)/(35*d)) - (A*4i)/(5*d) + ((28*A + 112*C)*1i)/(35*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(140*A + 96*C)*1i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
158,1,182,95,6.961036,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x),x)","-\frac{2\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}-1\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(A\,15{}\mathrm{i}+C\,8{}\mathrm{i}+A\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,30{}\mathrm{i}+A\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,15{}\mathrm{i}+C\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,8{}\mathrm{i}+C\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,28{}\mathrm{i}+C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}+C\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,8{}\mathrm{i}\right)}{15\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"-(2*(exp(c*1i + d*x*1i) - 1)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(A*15i + C*8i + A*exp(c*2i + d*x*2i)*30i + A*exp(c*4i + d*x*4i)*15i + C*exp(c*1i + d*x*1i)*8i + C*exp(c*2i + d*x*2i)*28i + C*exp(c*3i + d*x*3i)*8i + C*exp(c*4i + d*x*4i)*8i))/(15*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
159,0,-1,96,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
160,0,-1,94,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
161,0,-1,110,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
162,0,-1,153,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
163,0,-1,196,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
164,1,751,225,13.147528,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,a\,24{}\mathrm{i}}{7\,d}+\frac{a\,\left(A+12\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{C\,a\,416{}\mathrm{i}}{231\,d}\right)-\frac{a\,\left(3\,A+4\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{A\,a\,8{}\mathrm{i}}{7\,d}+\frac{C\,a\,32{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(5\,A+4\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a\,\left(7\,A+12\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{A\,a\,16{}\mathrm{i}}{11\,d}\right)+\frac{a\,\left(5\,A+4\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a\,\left(7\,A+12\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{A\,a\,16{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}+\frac{\left(\frac{A\,a\,8{}\mathrm{i}}{3\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(143\,A+112\,C\right)\,8{}\mathrm{i}}{1155\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a\,8{}\mathrm{i}}{3\,d}-\frac{a\,\left(A+3\,C\right)\,32{}\mathrm{i}}{9\,d}+\frac{a\,\left(A-8\,C\right)\,8{}\mathrm{i}}{9\,d}-\frac{C\,a\,64{}\mathrm{i}}{99\,d}\right)+\frac{a\,\left(3\,A+8\,C\right)\,8{}\mathrm{i}}{9\,d}-\frac{a\,\left(A+C\right)\,32{}\mathrm{i}}{9\,d}+\frac{A\,a\,8{}\mathrm{i}}{9\,d}+\frac{C\,a\,64{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(11\,A-14\,C\right)\,16{}\mathrm{i}}{385\,d}+\frac{A\,a\,24{}\mathrm{i}}{5\,d}\right)-\frac{A\,a\,8{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+2\,C\right)\,16{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(143\,A+112\,C\right)\,16{}\mathrm{i}}{1155\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(A + 12*C)*8i)/(7*d) - (A*a*24i)/(7*d) + (C*a*416i)/(231*d)) - (a*(3*A + 4*C)*8i)/(7*d) + (A*a*8i)/(7*d) + (C*a*32i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(5*A + 4*C)*8i)/(11*d) - (a*(7*A + 12*C)*8i)/(11*d) + (A*a*16i)/(11*d)) + (a*(5*A + 4*C)*8i)/(11*d) - (a*(7*A + 12*C)*8i)/(11*d) + (A*a*16i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) + (((A*a*8i)/(3*d) - (a*exp(c*1i + d*x*1i)*(143*A + 112*C)*8i)/(1155*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a*(3*A + 8*C)*8i)/(9*d) - exp(c*1i + d*x*1i)*((A*a*8i)/(3*d) - (a*(A + 3*C)*32i)/(9*d) + (a*(A - 8*C)*8i)/(9*d) - (C*a*64i)/(99*d)) - (a*(A + C)*32i)/(9*d) + (A*a*8i)/(9*d) + (C*a*64i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(11*A - 14*C)*16i)/(385*d) + (A*a*24i)/(5*d)) - (A*a*8i)/(5*d) + (a*(A + 2*C)*16i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(143*A + 112*C)*16i)/(1155*d*(exp(c*1i + d*x*1i) + 1))","B"
165,1,621,174,10.679174,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(5\,A+4\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a\,\left(7\,A+12\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{A\,a\,8{}\mathrm{i}}{9\,d}\right)-\frac{a\,\left(5\,A+4\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a\,\left(7\,A+12\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{A\,a\,8{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+4\,C\right)\,4{}\mathrm{i}}{5\,d}-\frac{A\,a\,4{}\mathrm{i}}{5\,d}+\frac{C\,a\,16{}\mathrm{i}}{105\,d}\right)-\frac{A\,a\,12{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+12\,C\right)\,4{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+8\,C\right)\,4{}\mathrm{i}}{7\,d}-\frac{a\,\left(A+C\right)\,16{}\mathrm{i}}{7\,d}+\frac{A\,a\,4{}\mathrm{i}}{7\,d}+\frac{C\,a\,32{}\mathrm{i}}{63\,d}\right)+\frac{A\,a\,12{}\mathrm{i}}{7\,d}-\frac{a\,\left(A+3\,C\right)\,16{}\mathrm{i}}{7\,d}+\frac{a\,\left(A-8\,C\right)\,4{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(21\,A+34\,C\right)\,8{}\mathrm{i}}{315\,d}-\frac{A\,a\,4{}\mathrm{i}}{3\,d}\right)-\frac{A\,a\,4{}\mathrm{i}}{d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(189\,A+136\,C\right)\,4{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(5*A + 4*C)*4i)/(9*d) - (a*(7*A + 12*C)*4i)/(9*d) + (A*a*8i)/(9*d)) - (a*(5*A + 4*C)*4i)/(9*d) + (a*(7*A + 12*C)*4i)/(9*d) - (A*a*8i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 4*C)*4i)/(5*d) - (A*a*4i)/(5*d) + (C*a*16i)/(105*d)) - (A*a*12i)/(5*d) + (a*(A + 12*C)*4i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 8*C)*4i)/(7*d) - (a*(A + C)*16i)/(7*d) + (A*a*4i)/(7*d) + (C*a*32i)/(63*d)) + (A*a*12i)/(7*d) - (a*(A + 3*C)*16i)/(7*d) + (a*(A - 8*C)*4i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(21*A + 34*C)*8i)/(315*d) - (A*a*4i)/(3*d)) - (A*a*4i)/d))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(189*A + 136*C)*4i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
166,1,510,132,6.797613,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x),x)","\frac{\left(\frac{A\,a\,2{}\mathrm{i}}{d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(175\,A+104\,C\right)\,2{}\mathrm{i}}{105\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(7\,A-8\,C\right)\,2{}\mathrm{i}}{35\,d}+\frac{A\,a\,6{}\mathrm{i}}{5\,d}-\frac{a\,\left(A+3\,C\right)\,8{}\mathrm{i}}{5\,d}\right)-\frac{a\,\left(3\,A+8\,C\right)\,2{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+C\right)\,8{}\mathrm{i}}{5\,d}-\frac{A\,a\,2{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(5\,A+4\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a\,\left(7\,A+12\,C\right)\,2{}\mathrm{i}}{7\,d}+\frac{A\,a\,4{}\mathrm{i}}{7\,d}\right)+\frac{a\,\left(5\,A+4\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a\,\left(7\,A+12\,C\right)\,2{}\mathrm{i}}{7\,d}+\frac{A\,a\,4{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(35\,A+52\,C\right)\,2{}\mathrm{i}}{105\,d}-\frac{A\,a\,2{}\mathrm{i}}{d}\right)-\frac{a\,\left(3\,A+4\,C\right)\,2{}\mathrm{i}}{3\,d}+\frac{A\,a\,2{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"(((A*a*2i)/d - (a*exp(c*1i + d*x*1i)*(175*A + 104*C)*2i)/(105*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/(exp(c*1i + d*x*1i) + 1) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(7*A - 8*C)*2i)/(35*d) + (A*a*6i)/(5*d) - (a*(A + 3*C)*8i)/(5*d)) - (a*(3*A + 8*C)*2i)/(5*d) + (a*(A + C)*8i)/(5*d) - (A*a*2i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(5*A + 4*C)*2i)/(7*d) - (a*(7*A + 12*C)*2i)/(7*d) + (A*a*4i)/(7*d)) + (a*(5*A + 4*C)*2i)/(7*d) - (a*(7*A + 12*C)*2i)/(7*d) + (A*a*4i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(35*A + 52*C)*2i)/(105*d) - (A*a*2i)/d) - (a*(3*A + 4*C)*2i)/(3*d) + (A*a*2i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
167,0,-1,133,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
168,0,-1,136,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
169,0,-1,151,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
170,0,-1,155,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
171,0,-1,200,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
172,0,-1,245,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
173,1,1039,273,12.780802,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,a^2\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(10439\,A+8368\,C\right)\,8{}\mathrm{i}}{45045\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,8{}\mathrm{i}}{d}+\frac{a^2\,\left(286\,A-523\,C\right)\,32{}\mathrm{i}}{15015\,d}\right)-\frac{A\,a^2\,8{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(2\,A+C\right)\,32{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,48{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(3\,A+C\right)\,32{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(13\,A+20\,C\right)\,16{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(A+C\right)\,160{}\mathrm{i}}{13\,d}\right)-\frac{A\,a^2\,48{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(3\,A+C\right)\,32{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(13\,A+20\,C\right)\,16{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(A+C\right)\,160{}\mathrm{i}}{13\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^6}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,40{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(A-16\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{C\,a^2\,128{}\mathrm{i}}{143\,d}-\frac{a^2\,\left(3\,A+4\,C\right)\,40{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(11\,A+20\,C\right)\,8{}\mathrm{i}}{11\,d}\right)-\frac{A\,a^2\,8{}\mathrm{i}}{11\,d}-\frac{C\,a^2\,128{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(11\,A+4\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(5\,A+12\,C\right)\,24{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(5\,A-16\,C\right)\,8{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,a^2\,40{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(A+4\,C\right)\,40{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(143\,A+811\,C\right)\,32{}\mathrm{i}}{9009\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(A-7\,C\right)\,32{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(9\,A+4\,C\right)\,8{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,16{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(A+2\,C\right)\,80{}\mathrm{i}}{9\,d}+\frac{C\,a^2\,128{}\mathrm{i}}{429\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{9\,d}+\frac{C\,a^2\,128{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(5\,A+2\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+32\,C\right)\,8{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(10439\,A+8368\,C\right)\,16{}\mathrm{i}}{45045\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a^2*8i)/(3*d) - (a^2*exp(c*1i + d*x*1i)*(10439*A + 8368*C)*8i)/(45045*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*8i)/d + (a^2*(286*A - 523*C)*32i)/(15015*d)) - (A*a^2*8i)/(5*d) + (a^2*(2*A + C)*32i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*48i)/(13*d) - (a^2*(3*A + C)*32i)/(13*d) + (a^2*(13*A + 20*C)*16i)/(13*d) - (a^2*(A + C)*160i)/(13*d)) - (A*a^2*48i)/(13*d) + (a^2*(3*A + C)*32i)/(13*d) - (a^2*(13*A + 20*C)*16i)/(13*d) + (a^2*(A + C)*160i)/(13*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^6) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*40i)/(11*d) - (a^2*(A - 16*C)*8i)/(11*d) + (C*a^2*128i)/(143*d) - (a^2*(3*A + 4*C)*40i)/(11*d) + (a^2*(11*A + 20*C)*8i)/(11*d)) - (A*a^2*8i)/(11*d) - (C*a^2*128i)/(11*d) + (a^2*(11*A + 4*C)*8i)/(11*d) - (a^2*(5*A + 12*C)*24i)/(11*d) + (a^2*(5*A - 16*C)*8i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(A + 4*C)*40i)/(7*d) - (A*a^2*40i)/(7*d) + (a^2*(143*A + 811*C)*32i)/(9009*d)) + (A*a^2*8i)/(7*d) - (a^2*(A - 7*C)*32i)/(7*d) - (a^2*(9*A + 4*C)*8i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a^2*8i)/(9*d) - exp(c*1i + d*x*1i)*((A*a^2*16i)/(3*d) - (a^2*(A + 2*C)*80i)/(9*d) + (C*a^2*128i)/(429*d)) + (C*a^2*128i)/(3*d) - (a^2*(5*A + 2*C)*16i)/(9*d) + (a^2*(5*A + 32*C)*8i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(10439*A + 8368*C)*16i)/(45045*d*(exp(c*1i + d*x*1i) + 1))","B"
174,1,885,211,15.862321,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,24{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(3\,A+C\right)\,16{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(13\,A+20\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(A+C\right)\,80{}\mathrm{i}}{11\,d}\right)+\frac{A\,a^2\,24{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(3\,A+C\right)\,16{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(13\,A+20\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(A+C\right)\,80{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{9\,d}+\frac{C\,a^2\,64{}\mathrm{i}}{99\,d}-\frac{a^2\,\left(11\,A+4\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+12\,C\right)\,4{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(5\,A-16\,C\right)\,4{}\mathrm{i}}{9\,d}\right)+\frac{A\,a^2\,20{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(A-16\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(3\,A+4\,C\right)\,20{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(11\,A+20\,C\right)\,4{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,a^2\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(9\,A+4\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(33\,A-31\,C\right)\,16{}\mathrm{i}}{1155\,d}\right)-\frac{A\,a^2\,4{}\mathrm{i}}{d}+\frac{a^2\,\left(A+4\,C\right)\,4{}\mathrm{i}}{d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{7\,d}+\frac{C\,a^2\,1600{}\mathrm{i}}{693\,d}-\frac{a^2\,\left(5\,A+2\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,A+32\,C\right)\,4{}\mathrm{i}}{7\,d}\right)+\frac{A\,a^2\,24{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(A+2\,C\right)\,40{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(66\,A+71\,C\right)\,16{}\mathrm{i}}{693\,d}\right)+\frac{A\,a^2\,20{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(759\,A+568\,C\right)\,4{}\mathrm{i}}{693\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*24i)/(11*d) - (a^2*(3*A + C)*16i)/(11*d) + (a^2*(13*A + 20*C)*8i)/(11*d) - (a^2*(A + C)*80i)/(11*d)) + (A*a^2*24i)/(11*d) - (a^2*(3*A + C)*16i)/(11*d) + (a^2*(13*A + 20*C)*8i)/(11*d) - (a^2*(A + C)*80i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(9*d) + (C*a^2*64i)/(99*d) - (a^2*(11*A + 4*C)*4i)/(9*d) + (a^2*(5*A + 12*C)*4i)/(3*d) - (a^2*(5*A - 16*C)*4i)/(9*d)) + (A*a^2*20i)/(9*d) - (a^2*(A - 16*C)*4i)/(9*d) - (a^2*(3*A + 4*C)*20i)/(9*d) + (a^2*(11*A + 20*C)*4i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(9*A + 4*C)*4i)/(5*d) - (A*a^2*4i)/(5*d) + (a^2*(33*A - 31*C)*16i)/(1155*d)) - (A*a^2*4i)/d + (a^2*(A + 4*C)*4i)/d))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(7*d) + (C*a^2*1600i)/(693*d) - (a^2*(5*A + 2*C)*8i)/(7*d) + (a^2*(5*A + 32*C)*4i)/(7*d)) + (A*a^2*24i)/(7*d) - (a^2*(A + 2*C)*40i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(3*d) - (a^2*(66*A + 71*C)*16i)/(693*d)) + (A*a^2*20i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(759*A + 568*C)*4i)/(693*d*(exp(c*1i + d*x*1i) + 1))","B"
175,1,766,169,11.203825,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x),x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,a^2\,2{}\mathrm{i}}{d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(903\,A+584\,C\right)\,2{}\mathrm{i}}{315\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,2{}\mathrm{i}}{d}-\frac{a^2\,\left(A+2\,C\right)\,4{}\mathrm{i}}{d}+\frac{a^2\,\left(21\,A-32\,C\right)\,2{}\mathrm{i}}{105\,d}\right)-\frac{A\,a^2\,2{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(5\,A+2\,C\right)\,4{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(5\,A+32\,C\right)\,2{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(3\,A+C\right)\,8{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(13\,A+20\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(A+C\right)\,40{}\mathrm{i}}{9\,d}\right)-\frac{A\,a^2\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,\left(3\,A+C\right)\,8{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(13\,A+20\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(A+C\right)\,40{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,10{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(189\,A+292\,C\right)\,2{}\mathrm{i}}{315\,d}\right)-\frac{A\,a^2\,2{}\mathrm{i}}{3\,d}+\frac{a^2\,\left(9\,A+4\,C\right)\,2{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(3\,A+4\,C\right)\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(9\,A-16\,C\right)\,2{}\mathrm{i}}{63\,d}+\frac{a^2\,\left(11\,A+20\,C\right)\,2{}\mathrm{i}}{7\,d}\right)-\frac{A\,a^2\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(11\,A+4\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+12\,C\right)\,6{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,A-16\,C\right)\,2{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a^2*2i)/d - (a^2*exp(c*1i + d*x*1i)*(903*A + 584*C)*2i)/(315*d)))/(exp(c*1i + d*x*1i) + 1) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*2i)/d - (a^2*(A + 2*C)*4i)/d + (a^2*(21*A - 32*C)*2i)/(105*d)) - (A*a^2*2i)/(5*d) + (a^2*(5*A + 2*C)*4i)/(5*d) - (a^2*(5*A + 32*C)*2i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(3*d) - (a^2*(3*A + C)*8i)/(9*d) + (a^2*(13*A + 20*C)*4i)/(9*d) - (a^2*(A + C)*40i)/(9*d)) - (A*a^2*4i)/(3*d) + (a^2*(3*A + C)*8i)/(9*d) - (a^2*(13*A + 20*C)*4i)/(9*d) + (a^2*(A + C)*40i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*10i)/(3*d) - (a^2*(189*A + 292*C)*2i)/(315*d)) - (A*a^2*2i)/(3*d) + (a^2*(9*A + 4*C)*2i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*10i)/(7*d) - (a^2*(3*A + 4*C)*10i)/(7*d) - (a^2*(9*A - 16*C)*2i)/(63*d) + (a^2*(11*A + 20*C)*2i)/(7*d)) - (A*a^2*2i)/(7*d) + (a^2*(11*A + 4*C)*2i)/(7*d) - (a^2*(5*A + 12*C)*6i)/(7*d) + (a^2*(5*A - 16*C)*2i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3)","B"
176,0,-1,170,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
177,0,-1,173,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
178,0,-1,188,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
179,0,-1,192,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
180,0,-1,200,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
181,0,-1,245,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
182,0,-1,290,0.000000,"\text{Not used}","int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^6\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
183,0,-1,236,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)), x)","F"
184,0,-1,193,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)), x)","F"
185,0,-1,152,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)), x)","F"
186,0,-1,109,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)), x)","F"
187,0,-1,115,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/2), x)","F"
188,0,-1,113,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
189,0,-1,159,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
190,0,-1,200,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
191,0,-1,243,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^4*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
192,0,-1,259,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)), x)","F"
193,0,-1,214,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)), x)","F"
194,0,-1,169,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)), x)","F"
195,0,-1,126,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)), x)","F"
196,0,-1,125,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(3/2), x)","F"
197,0,-1,158,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
198,0,-1,217,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
199,0,-1,266,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
200,0,-1,259,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)), x)","F"
201,0,-1,212,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)), x)","F"
202,0,-1,165,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)), x)","F"
203,0,-1,130,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)), x)","F"
204,0,-1,162,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/2), x)","F"
205,0,-1,199,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
206,0,-1,262,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
207,0,-1,205,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2), x)","F"
208,0,-1,172,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2), x)","F"
209,0,-1,135,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(1/2), x)","F"
210,0,-1,135,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(3/2), x)","F"
211,0,-1,141,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(5/2), x)","F"
212,0,-1,174,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(7/2), x)","F"
213,0,-1,205,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(9/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(9/2), x)","F"
214,0,-1,270,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2), x)","F"
215,0,-1,237,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2), x)","F"
216,0,-1,196,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2), x)","F"
217,0,-1,198,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2), x)","F"
218,0,-1,196,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(5/2), x)","F"
219,0,-1,204,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(7/2), x)","F"
220,0,-1,237,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(9/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(9/2), x)","F"
221,0,-1,270,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(11/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(11/2), x)","F"
222,0,-1,319,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2), x)","F"
223,0,-1,286,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2), x)","F"
224,0,-1,253,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2), x)","F"
225,0,-1,259,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2), x)","F"
226,0,-1,253,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(5/2), x)","F"
227,0,-1,253,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(7/2), x)","F"
228,0,-1,253,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(9/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(9/2), x)","F"
229,0,-1,286,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(11/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(11/2), x)","F"
230,0,-1,319,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(13/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(13/2), x)","F"
231,0,-1,232,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x)), x)","F"
232,0,-1,190,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x)), x)","F"
233,0,-1,152,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x)), x)","F"
234,0,-1,124,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
235,0,-1,162,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
236,0,-1,199,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)), x)","F"
237,0,-1,229,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^2, x)","F"
238,0,-1,191,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^2, x)","F"
239,0,-1,165,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^2, x)","F"
240,0,-1,170,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
241,0,-1,201,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
242,0,-1,236,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)), x)","F"
243,0,-1,282,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^3, x)","F"
244,0,-1,249,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^3, x)","F"
245,0,-1,220,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^3, x)","F"
246,0,-1,222,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^3, x)","F"
247,0,-1,226,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
248,0,-1,249,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
249,0,-1,290,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)), x)","F"
250,0,-1,214,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2), x)","F"
251,0,-1,169,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2), x)","F"
252,0,-1,124,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2), x)","F"
253,0,-1,115,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
254,0,-1,116,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2), x)","F"
255,1,94,122,3.861474,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(5/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(35\,A\,\sin\left(c+d\,x\right)+60\,C\,\sin\left(c+d\,x\right)+8\,A\,\sin\left(2\,c+2\,d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)\right)}{30\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(35*A*sin(c + d*x) + 60*C*sin(c + d*x) + 8*A*sin(2*c + 2*d*x) + 3*A*sin(3*c + 3*d*x)))/(30*d*(cos(c + d*x) + 1))","B"
256,1,118,168,4.543795,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(7/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(420\,A\,\sin\left(c+d\,x\right)+560\,C\,\sin\left(c+d\,x\right)+126\,A\,\sin\left(2\,c+2\,d\,x\right)+36\,A\,\sin\left(3\,c+3\,d\,x\right)+15\,A\,\sin\left(4\,c+4\,d\,x\right)+140\,C\,\sin\left(2\,c+2\,d\,x\right)\right)}{420\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(420*A*sin(c + d*x) + 560*C*sin(c + d*x) + 126*A*sin(2*c + 2*d*x) + 36*A*sin(3*c + 3*d*x) + 15*A*sin(4*c + 4*d*x) + 140*C*sin(2*c + 2*d*x)))/(420*d*(cos(c + d*x) + 1))","B"
257,1,142,213,5.516680,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(9/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(2310\,A\,\sin\left(c+d\,x\right)+2940\,C\,\sin\left(c+d\,x\right)+672\,A\,\sin\left(2\,c+2\,d\,x\right)+297\,A\,\sin\left(3\,c+3\,d\,x\right)+80\,A\,\sin\left(4\,c+4\,d\,x\right)+35\,A\,\sin\left(5\,c+5\,d\,x\right)+672\,C\,\sin\left(2\,c+2\,d\,x\right)+252\,C\,\sin\left(3\,c+3\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(2310*A*sin(c + d*x) + 2940*C*sin(c + d*x) + 672*A*sin(2*c + 2*d*x) + 297*A*sin(3*c + 3*d*x) + 80*A*sin(4*c + 4*d*x) + 35*A*sin(5*c + 5*d*x) + 672*C*sin(2*c + 2*d*x) + 252*C*sin(3*c + 3*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
258,0,-1,265,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2), x)","F"
259,0,-1,218,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2), x)","F"
260,0,-1,171,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2), x)","F"
261,0,-1,171,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
262,0,-1,169,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2), x)","F"
263,0,-1,163,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(5/2), x)","F"
264,1,119,169,4.664435,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(7/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(910\,A\,\sin\left(c+d\,x\right)+1400\,C\,\sin\left(c+d\,x\right)+238\,A\,\sin\left(2\,c+2\,d\,x\right)+78\,A\,\sin\left(3\,c+3\,d\,x\right)+15\,A\,\sin\left(4\,c+4\,d\,x\right)+140\,C\,\sin\left(2\,c+2\,d\,x\right)\right)}{420\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(910*A*sin(c + d*x) + 1400*C*sin(c + d*x) + 238*A*sin(2*c + 2*d*x) + 78*A*sin(3*c + 3*d*x) + 15*A*sin(4*c + 4*d*x) + 140*C*sin(2*c + 2*d*x)))/(420*d*(cos(c + d*x) + 1))","B"
265,1,143,219,5.679604,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(9/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(4830\,A\,\sin\left(c+d\,x\right)+6300\,C\,\sin\left(c+d\,x\right)+1428\,A\,\sin\left(2\,c+2\,d\,x\right)+513\,A\,\sin\left(3\,c+3\,d\,x\right)+170\,A\,\sin\left(4\,c+4\,d\,x\right)+35\,A\,\sin\left(5\,c+5\,d\,x\right)+1512\,C\,\sin\left(2\,c+2\,d\,x\right)+252\,C\,\sin\left(3\,c+3\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(4830*A*sin(c + d*x) + 6300*C*sin(c + d*x) + 1428*A*sin(2*c + 2*d*x) + 513*A*sin(3*c + 3*d*x) + 170*A*sin(4*c + 4*d*x) + 35*A*sin(5*c + 5*d*x) + 1512*C*sin(2*c + 2*d*x) + 252*C*sin(3*c + 3*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
266,1,374,266,9.138536,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(11/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{a\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(9\,A+10\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{12\,d}+\frac{a\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(7\,A+4\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{56\,d}+\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,A+14\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{4\,d}+\frac{a\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(13\,A+12\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{40\,d}+\frac{A\,a\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{24\,d}+\frac{A\,a\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{88\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((11*c)/2 + (11*d*x)/2)*1i + 2*sin((11*c)/4 + (11*d*x)/4)^2 - 1)*((a*sin((3*c)/2 + (3*d*x)/2)*(9*A + 10*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(12*d) + (a*sin((7*c)/2 + (7*d*x)/2)*(7*A + 4*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(56*d) + (a*sin(c/2 + (d*x)/2)*(11*A + 14*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(4*d) + (a*sin((5*c)/2 + (5*d*x)/2)*(13*A + 12*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(40*d) + (A*a*sin((9*c)/2 + (9*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(24*d) + (A*a*sin((11*c)/2 + (11*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(88*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
267,0,-1,312,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2), x)","F"
268,0,-1,265,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2), x)","F"
269,0,-1,218,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2), x)","F"
270,0,-1,218,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
271,0,-1,224,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)","F"
272,0,-1,210,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(5/2), x)","F"
273,0,-1,210,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(7/2), x)","F"
274,1,145,216,5.744084,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(9/2),x)","\frac{a^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(10290\,A\,\sin\left(c+d\,x\right)+14700\,C\,\sin\left(c+d\,x\right)+2856\,A\,\sin\left(2\,c+2\,d\,x\right)+981\,A\,\sin\left(3\,c+3\,d\,x\right)+260\,A\,\sin\left(4\,c+4\,d\,x\right)+35\,A\,\sin\left(5\,c+5\,d\,x\right)+2352\,C\,\sin\left(2\,c+2\,d\,x\right)+252\,C\,\sin\left(3\,c+3\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a^2*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(10290*A*sin(c + d*x) + 14700*C*sin(c + d*x) + 2856*A*sin(2*c + 2*d*x) + 981*A*sin(3*c + 3*d*x) + 260*A*sin(4*c + 4*d*x) + 35*A*sin(5*c + 5*d*x) + 2352*C*sin(2*c + 2*d*x) + 252*C*sin(3*c + 3*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
275,1,386,266,9.586001,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(11/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{5\,A\,a^2\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{72\,d}+\frac{A\,a^2\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{88\,d}+\frac{a^2\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(5\,A+4\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{8\,d}+\frac{a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(13\,A+4\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{56\,d}+\frac{a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(19\,A+22\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{12\,d}+\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,A+30\,C\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{4\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((11*c)/2 + (11*d*x)/2)*1i + 2*sin((11*c)/4 + (11*d*x)/4)^2 - 1)*((5*A*a^2*sin((9*c)/2 + (9*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(72*d) + (A*a^2*sin((11*c)/2 + (11*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(88*d) + (a^2*sin((5*c)/2 + (5*d*x)/2)*(5*A + 4*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(8*d) + (a^2*sin((7*c)/2 + (7*d*x)/2)*(13*A + 4*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(56*d) + (a^2*sin((3*c)/2 + (3*d*x)/2)*(19*A + 22*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(12*d) + (a^2*sin(c/2 + (d*x)/2)*(23*A + 30*C)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(4*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
276,1,437,313,10.734266,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(13/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{5\,A\,a^2\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{176\,d}+\frac{A\,a^2\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{208\,d}+\frac{5\,a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(3\,A+2\,C\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{56\,d}+\frac{a^2\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(7\,A+2\,C\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{72\,d}+\frac{3\,a^2\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(17\,A+16\,C\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{80\,d}+\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(21\,A+26\,C\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{4\,d}+\frac{a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(71\,A+80\,C\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{48\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((13*c)/2 + (13*d*x)/2)*1i + 2*sin((13*c)/4 + (13*d*x)/4)^2 - 1)*((5*A*a^2*sin((11*c)/2 + (11*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(176*d) + (A*a^2*sin((13*c)/2 + (13*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(208*d) + (5*a^2*sin((7*c)/2 + (7*d*x)/2)*(3*A + 2*C)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(56*d) + (a^2*sin((9*c)/2 + (9*d*x)/2)*(7*A + 2*C)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(72*d) + (3*a^2*sin((5*c)/2 + (5*d*x)/2)*(17*A + 16*C)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(80*d) + (a^2*sin(c/2 + (d*x)/2)*(21*A + 26*C)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(4*d) + (a^2*sin((3*c)/2 + (3*d*x)/2)*(71*A + 80*C)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(48*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
277,0,-1,226,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(1/2), x)","F"
278,0,-1,183,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(1/2), x)","F"
279,0,-1,133,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(1/2), x)","F"
280,0,-1,135,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
281,0,-1,136,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
282,0,-1,181,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
283,0,-1,224,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)), x)","F"
284,0,-1,188,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(3/2), x)","F"
285,0,-1,145,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(3/2), x)","F"
286,0,-1,152,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
287,0,-1,201,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
288,0,-1,248,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
289,0,-1,237,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
290,0,-1,192,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
291,0,-1,154,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
292,0,-1,199,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
293,0,-1,246,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
294,0,-1,295,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)), x)","F"
295,0,-1,434,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(2/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(2/3), x)","F"
296,0,-1,384,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/3), x)","F"
297,0,-1,396,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(4/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(4/3), x)","F"
298,0,-1,457,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(7/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(7/3), x)","F"
299,0,-1,815,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(4/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(4/3), x)","F"
300,0,-1,774,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/3), x)","F"
301,0,-1,791,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(2/3), x)","F"
302,0,-1,841,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/3), x)","F"
303,0,-1,244,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^n*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^n*(1/cos(c + d*x))^m, x)","F"
304,0,-1,253,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^n)/(1/cos(c + d*x))^(n + 1),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{n+1}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^n)/(1/cos(c + d*x))^(n + 1), x)","F"
305,0,-1,38,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^n)/(1/cos(c + d*x))^(n + 1) - ((a + a/cos(c + d*x))^n*(A*a*n + (C*a*(n + 1))/cos(c + d*x)))/(a*(1/cos(c + d*x))^n*(n + 1)),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{n+1}}-\frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A\,a\,n+\frac{C\,a\,\left(n+1\right)}{\cos\left(c+d\,x\right)}\right)}{a\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^n\,\left(n+1\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^n)/(1/cos(c + d*x))^(n + 1) - ((a + a/cos(c + d*x))^n*(A*a*n + (C*a*(n + 1))/cos(c + d*x)))/(a*(1/cos(c + d*x))^n*(n + 1)), x)","F"
306,1,166,106,5.335566,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(-B\,a-\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{7\,B\,a}{3}+\frac{49\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{13\,B\,a}{3}-\frac{31\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,B+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*B*a + (13*C*a)/4) - tan(c/2 + (d*x)/2)^7*(B*a + (3*C*a)/4) - tan(c/2 + (d*x)/2)^3*((13*B*a)/3 + (31*C*a)/12) + tan(c/2 + (d*x)/2)^5*((7*B*a)/3 + (49*C*a)/12))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(4*B + 3*C))/(4*d)","B"
307,1,126,86,4.757617,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x),x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B+C\right)}{d}-\frac{\left(B\,a+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,B\,a-\frac{4\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B\,a+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(B + C))/d - (tan(c/2 + (d*x)/2)*(3*B*a + 3*C*a) + tan(c/2 + (d*x)/2)^5*(B*a + C*a) - tan(c/2 + (d*x)/2)^3*(4*B*a + (4*C*a)/3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
308,1,94,56,3.540865,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a+3\,C\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,a+C\,a\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,B+C\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*B*a + 3*C*a) - tan(c/2 + (d*x)/2)^3*(2*B*a + C*a))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(2*B + C))/d","B"
309,1,100,32,2.999374,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{C\,a\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(C*a*tan(c + d*x))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
310,1,100,32,3.016687,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(B*a*sin(c + d*x))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
311,1,50,47,2.830708,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{B\,a\,x}{2}+C\,a\,x+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(B*a*x)/2 + C*a*x + (B*a*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (B*a*sin(2*c + 2*d*x))/(4*d)","B"
312,1,84,77,2.857195,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{B\,a\,x}{2}+\frac{C\,a\,x}{2}+\frac{3\,B\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(B*a*x)/2 + (C*a*x)/2 + (3*B*a*sin(c + d*x))/(4*d) + (C*a*sin(c + d*x))/d + (B*a*sin(2*c + 2*d*x))/(4*d) + (B*a*sin(3*c + 3*d*x))/(12*d) + (C*a*sin(2*c + 2*d*x))/(4*d)","B"
313,1,184,97,5.422260,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{\left(\frac{3\,B\,a}{4}+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{49\,B\,a}{12}+\frac{7\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{31\,B\,a}{12}+\frac{13\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,B\,a}{4}+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B+4\,C\right)}{4\,\left(\frac{3\,B\,a}{4}+C\,a\right)}\right)\,\left(3\,B+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*B*a)/4 + 3*C*a) + tan(c/2 + (d*x)/2)^7*((3*B*a)/4 + C*a) + tan(c/2 + (d*x)/2)^3*((31*B*a)/12 + (13*C*a)/3) + tan(c/2 + (d*x)/2)^5*((49*B*a)/12 + (7*C*a)/3))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(3*B + 4*C))/(4*((3*B*a)/4 + C*a)))*(3*B + 4*C))/(4*d)","B"
314,1,224,169,5.643586,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,B+6\,C\right)}{4\,d}-\frac{\left(\frac{7\,B\,a^2}{4}+\frac{3\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{49\,B\,a^2}{6}-7\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{40\,B\,a^2}{3}+\frac{72\,C\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{79\,B\,a^2}{6}-9\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,B\,a^2}{4}+\frac{13\,C\,a^2}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^2*atanh(tan(c/2 + (d*x)/2))*(7*B + 6*C))/(4*d) - (tan(c/2 + (d*x)/2)*((25*B*a^2)/4 + (13*C*a^2)/2) + tan(c/2 + (d*x)/2)^9*((7*B*a^2)/4 + (3*C*a^2)/2) - tan(c/2 + (d*x)/2)^7*((49*B*a^2)/6 + 7*C*a^2) - tan(c/2 + (d*x)/2)^3*((79*B*a^2)/6 + 9*C*a^2) + tan(c/2 + (d*x)/2)^5*((40*B*a^2)/3 + (72*C*a^2)/5))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
315,1,183,138,5.302684,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/cos(c + d*x),x)","\frac{\left(-2\,B\,a^2-\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{22\,B\,a^2}{3}+\frac{77\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{34\,B\,a^2}{3}-\frac{83\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,B\,a^2+\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B+\frac{7\,C}{8}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(6*B*a^2 + (25*C*a^2)/4) - tan(c/2 + (d*x)/2)^7*(2*B*a^2 + (7*C*a^2)/4) + tan(c/2 + (d*x)/2)^5*((22*B*a^2)/3 + (77*C*a^2)/12) - tan(c/2 + (d*x)/2)^3*((34*B*a^2)/3 + (83*C*a^2)/12))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (2*a^2*atanh(tan(c/2 + (d*x)/2))*(B + (7*C)/8))/d","B"
316,1,145,103,4.724760,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,B}{2}+C\right)}{d}-\frac{\left(3\,B\,a^2+2\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,B\,a^2-\frac{16\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(5\,B\,a^2+6\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a^2*atanh(tan(c/2 + (d*x)/2))*((3*B)/2 + C))/d - (tan(c/2 + (d*x)/2)*(5*B*a^2 + 6*C*a^2) + tan(c/2 + (d*x)/2)^5*(3*B*a^2 + 2*C*a^2) - tan(c/2 + (d*x)/2)^3*(8*B*a^2 + (16*C*a^2)/3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
317,1,162,82,2.898553,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(2*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (2*C*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^2*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
318,1,161,73,2.932399,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{4\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(B*a^2*sin(c + d*x))/d + (4*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
319,1,141,88,2.976402,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(2*B*a^2*sin(c + d*x))/d + (C*a^2*sin(c + d*x))/d + (3*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^2*sin(2*c + 2*d*x))/(4*d)","B"
320,1,98,102,2.870422,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","B\,a^2\,x+\frac{3\,C\,a^2\,x}{2}+\frac{7\,B\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"B*a^2*x + (3*C*a^2*x)/2 + (7*B*a^2*sin(c + d*x))/(4*d) + (2*C*a^2*sin(c + d*x))/d + (B*a^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*sin(3*c + 3*d*x))/(12*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d)","B"
321,1,134,135,2.952445,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{7\,B\,a^2\,x}{8}+C\,a^2\,x+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{7\,C\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{B\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(7*B*a^2*x)/8 + C*a^2*x + (3*B*a^2*sin(c + d*x))/(2*d) + (7*C*a^2*sin(c + d*x))/(4*d) + (B*a^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*sin(3*c + 3*d*x))/(6*d) + (B*a^2*sin(4*c + 4*d*x))/(32*d) + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(12*d)","B"
322,1,247,160,5.669462,"\text{Not used}","int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{\left(\frac{3\,B\,a^2}{2}+\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(7\,B\,a^2+\frac{49\,C\,a^2}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{72\,B\,a^2}{5}+\frac{40\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(9\,B\,a^2+\frac{79\,C\,a^2}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,B\,a^2}{2}+\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,B+7\,C\right)}{4\,\left(\frac{3\,B\,a^2}{2}+\frac{7\,C\,a^2}{4}\right)}\right)\,\left(6\,B+7\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*B*a^2)/2 + (25*C*a^2)/4) + tan(c/2 + (d*x)/2)^9*((3*B*a^2)/2 + (7*C*a^2)/4) + tan(c/2 + (d*x)/2)^7*(7*B*a^2 + (49*C*a^2)/6) + tan(c/2 + (d*x)/2)^3*(9*B*a^2 + (79*C*a^2)/6) + tan(c/2 + (d*x)/2)^5*((72*B*a^2)/5 + (40*C*a^2)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(6*B + 7*C))/(4*((3*B*a^2)/2 + (7*C*a^2)/4)))*(6*B + 7*C))/(4*d)","B"
323,1,224,163,5.520491,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/cos(c + d*x),x)","\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,B+13\,C\right)}{4\,d}-\frac{\left(\frac{15\,B\,a^3}{4}+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{35\,B\,a^3}{2}-\frac{91\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(32\,B\,a^3+\frac{416\,C\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{61\,B\,a^3}{2}-\frac{133\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,B\,a^3}{4}+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh(tan(c/2 + (d*x)/2))*(15*B + 13*C))/(4*d) - (tan(c/2 + (d*x)/2)*((49*B*a^3)/4 + (51*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((15*B*a^3)/4 + (13*C*a^3)/4) - tan(c/2 + (d*x)/2)^7*((35*B*a^3)/2 + (91*C*a^3)/6) - tan(c/2 + (d*x)/2)^3*((61*B*a^3)/2 + (133*C*a^3)/6) + tan(c/2 + (d*x)/2)^5*(32*B*a^3 + (416*C*a^3)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
324,1,185,125,5.416319,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{\left(-5\,B\,a^3-\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{55\,B\,a^3}{3}+\frac{55\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{73\,B\,a^3}{3}-\frac{73\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,B\,a^3+\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{5\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,B+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(11*B*a^3 + (49*C*a^3)/4) - tan(c/2 + (d*x)/2)^7*(5*B*a^3 + (15*C*a^3)/4) + tan(c/2 + (d*x)/2)^5*((55*B*a^3)/3 + (55*C*a^3)/4) - tan(c/2 + (d*x)/2)^3*((73*B*a^3)/3 + (73*C*a^3)/4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (5*a^3*atanh(tan(c/2 + (d*x)/2))*(4*B + 3*C))/(4*d)","B"
325,1,209,111,3.007165,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{2\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{5\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{11\,C\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(2*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (5*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*B*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (11*C*a^3*sin(c + d*x))/(3*d*cos(c + d*x)) + (3*C*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (C*a^3*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
326,1,207,108,3.061461,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{6\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(B*a^3*sin(c + d*x))/d + (6*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (3*C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
327,1,197,117,3.026722,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{7\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(3*B*a^3*sin(c + d*x))/d + (C*a^3*sin(c + d*x))/d + (7*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
328,1,178,125,3.054449,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{15\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(15*B*a^3*sin(c + d*x))/(4*d) + (3*C*a^3*sin(c + d*x))/d + (5*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*B*a^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(3*c + 3*d*x))/(12*d) + (C*a^3*sin(2*c + 2*d*x))/(4*d)","B"
329,1,134,124,2.838120,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{15\,B\,a^3\,x}{8}+\frac{5\,C\,a^3\,x}{2}+\frac{13\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{15\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(15*B*a^3*x)/8 + (5*C*a^3*x)/2 + (13*B*a^3*sin(c + d*x))/(4*d) + (15*C*a^3*sin(c + d*x))/(4*d) + (B*a^3*sin(2*c + 2*d*x))/d + (B*a^3*sin(3*c + 3*d*x))/(4*d) + (B*a^3*sin(4*c + 4*d*x))/(32*d) + (3*C*a^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(3*c + 3*d*x))/(12*d)","B"
330,1,247,176,5.601616,"\text{Not used}","int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{13\,B\,a^3}{4}+\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{91\,B\,a^3}{6}+\frac{35\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,B\,a^3}{15}+32\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{133\,B\,a^3}{6}+\frac{61\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,B\,a^3}{4}+\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,B+15\,C\right)}{4\,\left(\frac{13\,B\,a^3}{4}+\frac{15\,C\,a^3}{4}\right)}\right)\,\left(13\,B+15\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*B*a^3)/4 + (49*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((13*B*a^3)/4 + (15*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((91*B*a^3)/6 + (35*C*a^3)/2) + tan(c/2 + (d*x)/2)^3*((133*B*a^3)/6 + (61*C*a^3)/2) + tan(c/2 + (d*x)/2)^5*((416*B*a^3)/15 + 32*C*a^3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(13*B + 15*C))/(4*((13*B*a^3)/4 + (15*C*a^3)/4)))*(13*B + 15*C))/(4*d)","B"
331,1,285,201,5.706659,"\text{Not used}","int(cos(c + d*x)^7*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{23\,B\,a^3}{8}+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{391\,B\,a^3}{24}+\frac{221\,C\,a^3}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{759\,B\,a^3}{20}+\frac{429\,C\,a^3}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{969\,B\,a^3}{20}+\frac{499\,C\,a^3}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{211\,B\,a^3}{8}+\frac{419\,C\,a^3}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{105\,B\,a^3}{8}+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,B+26\,C\right)}{8\,\left(\frac{23\,B\,a^3}{8}+\frac{13\,C\,a^3}{4}\right)}\right)\,\left(23\,B+26\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((105*B*a^3)/8 + (51*C*a^3)/4) + tan(c/2 + (d*x)/2)^11*((23*B*a^3)/8 + (13*C*a^3)/4) + tan(c/2 + (d*x)/2)^3*((211*B*a^3)/8 + (419*C*a^3)/12) + tan(c/2 + (d*x)/2)^9*((391*B*a^3)/24 + (221*C*a^3)/12) + tan(c/2 + (d*x)/2)^7*((759*B*a^3)/20 + (429*C*a^3)/10) + tan(c/2 + (d*x)/2)^5*((969*B*a^3)/20 + (499*C*a^3)/10))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(23*B + 26*C))/(8*((23*B*a^3)/8 + (13*C*a^3)/4)))*(23*B + 26*C))/(8*d)","B"
332,1,152,131,3.255165,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-C\right)}{a\,d}-\frac{\left(3\,B-5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,C}{3}-4\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B-3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2))*(B - C))/(a*d) - (tan(c/2 + (d*x)/2)^5*(3*B - 5*C) - tan(c/2 + (d*x)/2)^3*(4*B - (16*C)/3) + tan(c/2 + (d*x)/2)*(B - 3*C))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6)) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
333,1,119,108,3.035652,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-\frac{3\,C}{2}\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-3\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-C\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(tan(c/2 + (d*x)/2)*(B - C))/(a*d) - (2*atanh(tan(c/2 + (d*x)/2))*(B - (3*C)/2))/(a*d) - (tan(c/2 + (d*x)/2)^3*(2*B - 3*C) - tan(c/2 + (d*x)/2)*(2*B - C))/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4))","B"
334,1,79,62,2.839600,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))),x)","\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-C\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(2*C*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) + (2*atanh(tan(c/2 + (d*x)/2))*(B - C))/(a*d) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
335,1,41,44,2.830980,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x)),x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/(a*d) + (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
336,1,32,35,2.816225,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a}-\frac{B\,d\,x}{a}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)*(B - C))/a - (B*d*x)/a)/d","B"
337,1,65,60,2.913032,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{x\,\left(B-C\right)}{a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(2*B*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - (x*(B - C))/a + (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
338,1,107,98,3.139194,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{x\,\left(3\,B-2\,C\right)}{2\,a}-\frac{\left(3\,B-2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B-2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(x*(3*B - 2*C))/(2*a) - (tan(c/2 + (d*x)/2)^3*(3*B - 2*C) + tan(c/2 + (d*x)/2)*(B - 2*C))/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
339,1,138,122,3.967776,"\text{Not used}","int((cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{\left(5\,B-3\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,B}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B-C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{3\,x\,\left(B-C\right)}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(5*B - 3*C) + tan(c/2 + (d*x)/2)^3*((16*B)/3 - 4*C) + tan(c/2 + (d*x)/2)*(3*B - C))/(d*(a + 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6)) - (3*x*(B - C))/(2*a) + (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
340,1,166,156,2.898877,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^2}+\frac{2\,B-4\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-5\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-3\,C\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,B-7\,C\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^2) + (2*B - 4*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(2*B - 5*C) - tan(c/2 + (d*x)/2)*(2*B - 3*C))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) + (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) - (atanh(tan(c/2 + (d*x)/2))*(4*B - 7*C))/(a^2*d)","B"
341,1,120,108,2.859538,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^2),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-2\,C\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-C}{a^2}+\frac{B-3\,C}{2\,a^2}\right)}{d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(B - 2*C))/(a^2*d) - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) - (tan(c/2 + (d*x)/2)*((B - C)/a^2 + (B - 3*C)/(2*a^2)))/d - (2*C*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2))","B"
342,1,74,79,2.798130,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{C}{a^2}-\frac{B-C}{2\,a^2}\right)}{d}+\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) - (tan(c/2 + (d*x)/2)*(C/a^2 - (B - C)/(2*a^2)))/d + (2*C*atanh(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
343,1,45,62,2.709305,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B+C\right)}{2\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(B + C))/(2*a^2*d) - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
344,1,65,70,2.732702,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{3\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,B\,d\,x}{6\,a^2\,d}","Not used",1,"(3*C*tan(c/2 + (d*x)/2) - 9*B*tan(c/2 + (d*x)/2) + B*tan(c/2 + (d*x)/2)^3 - C*tan(c/2 + (d*x)/2)^3 + 6*B*d*x)/(6*a^2*d)","B"
345,1,109,98,2.812248,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-C}{a^2}+\frac{3\,B-C}{2\,a^2}\right)}{d}-\frac{x\,\left(2\,B-C\right)}{a^2}+\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((B - C)/a^2 + (3*B - C)/(2*a^2)))/d - (x*(2*B - C))/a^2 + (2*B*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
346,1,154,143,2.848286,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{x\,\left(7\,B-4\,C\right)}{2\,a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^2}+\frac{4\,B-2\,C}{2\,a^2}\right)}{d}-\frac{\left(5\,B-2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B-2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(x*(7*B - 4*C))/(2*a^2) - (tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^2) + (4*B - 2*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(5*B - 2*C) + tan(c/2 + (d*x)/2)*(3*B - 2*C))/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2)) + (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
347,1,187,170,2.895869,"\text{Not used}","int((cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{\left(10\,B-5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{40\,B}{3}-8\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,B-3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{x\,\left(10\,B-7\,C\right)}{2\,a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(B-C\right)}{a^2}+\frac{5\,B-3\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(10*B - 5*C) + tan(c/2 + (d*x)/2)^3*((40*B)/3 - 8*C) + tan(c/2 + (d*x)/2)*(6*B - 3*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2)) - (x*(10*B - 7*C))/(2*a^2) + (tan(c/2 + (d*x)/2)*((2*(B - C))/a^2 + (5*B - 3*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
348,1,216,202,2.840535,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^3}+\frac{3\,\left(3\,B-5\,C\right)}{4\,a^3}+\frac{2\,B-10\,C}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-7\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-5\,C\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{4\,a^3}+\frac{3\,B-5\,C}{12\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(6\,B-13\,C\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^3) + (3*(3*B - 5*C))/(4*a^3) + (2*B - 10*C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(2*B - 7*C) - tan(c/2 + (d*x)/2)*(2*B - 5*C))/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) + (tan(c/2 + (d*x)/2)^3*((B - C)/(4*a^3) + (3*B - 5*C)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d) - (atanh(tan(c/2 + (d*x)/2))*(6*B - 13*C))/(a^3*d)","B"
349,1,168,156,2.862085,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^3),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-3\,C\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{4\,a^3}-\frac{3\,C}{2\,a^3}+\frac{2\,B-4\,C}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{6\,a^3}+\frac{2\,B-4\,C}{12\,a^3}\right)}{d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(B - 3*C))/(a^3*d) - (tan(c/2 + (d*x)/2)*((3*(B - C))/(4*a^3) - (3*C)/(2*a^3) + (2*B - 4*C)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d) - (tan(c/2 + (d*x)/2)^3*((B - C)/(6*a^3) + (2*B - 4*C)/(12*a^3)))/d - (2*C*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3))","B"
350,1,124,125,2.900822,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{12\,a^3}+\frac{B-3\,C}{12\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-C}{4\,a^3}+\frac{B-3\,C}{4\,a^3}-\frac{B+3\,C}{4\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}+\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((B - C)/(12*a^3) + (B - 3*C)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((B - C)/(4*a^3) + (B - 3*C)/(4*a^3) - (B + 3*C)/(4*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d) + (2*C*atanh(tan(c/2 + (d*x)/2)))/(a^3*d)","B"
351,1,66,102,2.853340,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,B+15\,C-3\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(15*B + 15*C - 3*B*tan(c/2 + (d*x)/2)^4 + 10*C*tan(c/2 + (d*x)/2)^2 + 3*C*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
352,1,66,102,2.863065,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,B+15\,C-10\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(15*B + 15*C - 10*B*tan(c/2 + (d*x)/2)^2 + 3*B*tan(c/2 + (d*x)/2)^4 - 3*C*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
353,1,133,108,3.057046,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{B\,x}{a^3}+\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{7\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(B*x)/a^3 + (cos(c/2 + (d*x)/2)^2*((B*sin(c/2 + (d*x)/2)^3)/3 - (C*sin(c/2 + (d*x)/2)^3)/6) - cos(c/2 + (d*x)/2)^4*((7*B*sin(c/2 + (d*x)/2))/4 - (C*sin(c/2 + (d*x)/2))/4) - (B*sin(c/2 + (d*x)/2)^5)/20 + (C*sin(c/2 + (d*x)/2)^5)/20)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
354,1,155,136,2.955285,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,B}{2\,a^3}+\frac{3\,\left(B-C\right)}{4\,a^3}+\frac{4\,B-2\,C}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{6\,a^3}+\frac{4\,B-2\,C}{12\,a^3}\right)}{d}-\frac{x\,\left(3\,B-C\right)}{a^3}+\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*B)/(2*a^3) + (3*(B - C))/(4*a^3) + (4*B - 2*C)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((B - C)/(6*a^3) + (4*B - 2*C)/(12*a^3)))/d - (x*(3*B - C))/a^3 + (2*B*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 + a^3)) + (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d)","B"
355,1,204,187,3.053214,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{x\,\left(13\,B-6\,C\right)}{2\,a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^3}+\frac{3\,\left(5\,B-3\,C\right)}{4\,a^3}+\frac{10\,B-2\,C}{4\,a^3}\right)}{d}-\frac{\left(7\,B-2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(5\,B-2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{4\,a^3}+\frac{5\,B-3\,C}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}","Not used",1,"(x*(13*B - 6*C))/(2*a^3) - (tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^3) + (3*(5*B - 3*C))/(4*a^3) + (10*B - 2*C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(7*B - 2*C) + tan(c/2 + (d*x)/2)*(5*B - 2*C))/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3)) + (tan(c/2 + (d*x)/2)^3*((B - C)/(4*a^3) + (5*B - 3*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d)","B"
356,1,626,230,12.326854,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{B\,32{}\mathrm{i}}{9\,d}+\frac{C\,128{}\mathrm{i}}{9\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{C\,256{}\mathrm{i}}{33\,d}+\frac{\left(352\,B+704\,C\right)\,1{}\mathrm{i}}{99\,d}\right)\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{B\,32{}\mathrm{i}}{11\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,32{}\mathrm{i}}{11\,d}-\frac{\left(32\,B+64\,C\right)\,1{}\mathrm{i}}{11\,d}\right)-\frac{\left(32\,B+64\,C\right)\,1{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}+\frac{\left(\frac{B\,32{}\mathrm{i}}{5\,d}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(352\,B+320\,C\right)\,1{}\mathrm{i}}{1155\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{\left(352\,B+896\,C\right)\,1{}\mathrm{i}}{693\,d}+\frac{\left(3168\,B+6336\,C\right)\,1{}\mathrm{i}}{693\,d}\right)+\frac{B\,32{}\mathrm{i}}{7\,d}+\frac{\left(3168\,B-6336\,C\right)\,1{}\mathrm{i}}{693\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(2816\,B+2560\,C\right)\,1{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(1408\,B+1280\,C\right)\,1{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"(((B*32i)/(5*d) - (exp(c*1i + d*x*1i)*(352*B + 320*C)*1i)/(1155*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((B*32i)/(11*d) + exp(c*1i + d*x*1i)*((B*32i)/(11*d) - ((32*B + 64*C)*1i)/(11*d)) - ((32*B + 64*C)*1i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((C*128i)/(9*d) - (B*32i)/(9*d) + exp(c*1i + d*x*1i)*((C*256i)/(33*d) + ((352*B + 704*C)*1i)/(99*d))))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((B*32i)/(7*d) - exp(c*1i + d*x*1i)*(((352*B + 896*C)*1i)/(693*d) + ((3168*B + 6336*C)*1i)/(693*d)) + ((3168*B - 6336*C)*1i)/(693*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2816*B + 2560*C)*1i)/(3465*d*(exp(c*1i + d*x*1i) + 1)) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1408*B + 1280*C)*1i)/(3465*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
357,1,512,187,12.402663,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,16{}\mathrm{i}}{5\,d}+\frac{\left(48\,B-32\,C\right)\,1{}\mathrm{i}}{105\,d}\right)+\frac{\left(336\,B+672\,C\right)\,1{}\mathrm{i}}{105\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,16{}\mathrm{i}}{7\,d}-\frac{C\,320{}\mathrm{i}}{63\,d}\right)+\frac{C\,32{}\mathrm{i}}{7\,d}+\frac{\left(144\,B+288\,C\right)\,1{}\mathrm{i}}{63\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{B\,16{}\mathrm{i}}{9\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,16{}\mathrm{i}}{9\,d}-\frac{\left(16\,B+32\,C\right)\,1{}\mathrm{i}}{9\,d}\right)+\frac{\left(16\,B+32\,C\right)\,1{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(288\,B+256\,C\right)\,1{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(144\,B+128\,C\right)\,1{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*16i)/(5*d) + ((48*B - 32*C)*1i)/(105*d)) + ((336*B + 672*C)*1i)/(105*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*16i)/(7*d) - (C*320i)/(63*d)) + (C*32i)/(7*d) + ((144*B + 288*C)*1i)/(63*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*16i)/(9*d) - ((16*B + 32*C)*1i)/(9*d)) - (B*16i)/(9*d) + ((16*B + 32*C)*1i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(288*B + 256*C)*1i)/(315*d*(exp(c*1i + d*x*1i) + 1)) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(144*B + 128*C)*1i)/(315*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
358,1,407,144,6.769087,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{B\,8{}\mathrm{i}}{5\,d}+\frac{C\,16{}\mathrm{i}}{5\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{C\,16{}\mathrm{i}}{35\,d}+\frac{\left(56\,B+112\,C\right)\,1{}\mathrm{i}}{35\,d}\right)\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{B\,8{}\mathrm{i}}{7\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,8{}\mathrm{i}}{7\,d}-\frac{\left(8\,B+16\,C\right)\,1{}\mathrm{i}}{7\,d}\right)-\frac{\left(8\,B+16\,C\right)\,1{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left(\frac{B\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(56\,B+48\,C\right)\,1{}\mathrm{i}}{105\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(112\,B+96\,C\right)\,1{}\mathrm{i}}{105\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((C*16i)/(5*d) - (B*8i)/(5*d) + exp(c*1i + d*x*1i)*((C*16i)/(35*d) + ((56*B + 112*C)*1i)/(35*d))))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((B*8i)/(7*d) + exp(c*1i + d*x*1i)*((B*8i)/(7*d) - ((8*B + 16*C)*1i)/(7*d)) - ((8*B + 16*C)*1i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + (((B*8i)/(3*d) - (exp(c*1i + d*x*1i)*(56*B + 48*C)*1i)/(105*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(112*B + 96*C)*1i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
359,1,212,101,7.245094,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x),x)","-\frac{4\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}-1\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(B\,5{}\mathrm{i}+C\,4{}\mathrm{i}+B\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,5{}\mathrm{i}+B\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,10{}\mathrm{i}+B\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,5{}\mathrm{i}+B\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,5{}\mathrm{i}+C\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,4{}\mathrm{i}+C\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,14{}\mathrm{i}+C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,4{}\mathrm{i}+C\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,4{}\mathrm{i}\right)}{15\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"-(4*(exp(c*1i + d*x*1i) - 1)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(B*5i + C*4i + B*exp(c*1i + d*x*1i)*5i + B*exp(c*2i + d*x*2i)*10i + B*exp(c*3i + d*x*3i)*5i + B*exp(c*4i + d*x*4i)*5i + C*exp(c*1i + d*x*1i)*4i + C*exp(c*2i + d*x*2i)*14i + C*exp(c*3i + d*x*3i)*4i + C*exp(c*4i + d*x*4i)*4i))/(15*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
360,1,159,62,4.765968,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\frac{2\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(6\,B\,\sin\left(c+d\,x\right)+6\,C\,\sin\left(c+d\,x\right)+6\,B\,\sin\left(2\,c+2\,d\,x\right)+6\,B\,\sin\left(3\,c+3\,d\,x\right)+3\,B\,\sin\left(4\,c+4\,d\,x\right)+8\,C\,\sin\left(2\,c+2\,d\,x\right)+6\,C\,\sin\left(3\,c+3\,d\,x\right)+2\,C\,\sin\left(4\,c+4\,d\,x\right)\right)}{3\,d\,\left(12\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+4\,\cos\left(3\,c+3\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)+7\right)}","Not used",1,"(2*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(6*B*sin(c + d*x) + 6*C*sin(c + d*x) + 6*B*sin(2*c + 2*d*x) + 6*B*sin(3*c + 3*d*x) + 3*B*sin(4*c + 4*d*x) + 8*C*sin(2*c + 2*d*x) + 6*C*sin(3*c + 3*d*x) + 2*C*sin(4*c + 4*d*x)))/(3*d*(12*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 4*cos(3*c + 3*d*x) + cos(4*c + 4*d*x) + 7))","B"
361,0,-1,66,0.000000,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
362,0,-1,68,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
363,0,-1,117,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
364,0,-1,160,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
365,1,720,234,13.513130,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{B\,a\,16{}\mathrm{i}}{9\,d}+\frac{C\,a\,256{}\mathrm{i}}{33\,d}+\frac{a\,\left(B+2\,C\right)\,16{}\mathrm{i}}{3\,d}\right)-\frac{a\,\left(3\,B+2\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{C\,a\,64{}\mathrm{i}}{9\,d}+\frac{a\,\left(B+4\,C\right)\,16{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(11\,B-42\,C\right)\,16{}\mathrm{i}}{1155\,d}+\frac{B\,a\,16{}\mathrm{i}}{5\,d}\right)+\frac{a\,\left(3\,B+2\,C\right)\,16{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a\,\left(2\,B+3\,C\right)\,32{}\mathrm{i}}{11\,d}+\frac{a\,\left(3\,B+2\,C\right)\,16{}\mathrm{i}}{11\,d}+\frac{B\,a\,16{}\mathrm{i}}{11\,d}\right)-\frac{a\,\left(2\,B+3\,C\right)\,32{}\mathrm{i}}{11\,d}+\frac{a\,\left(3\,B+2\,C\right)\,16{}\mathrm{i}}{11\,d}+\frac{B\,a\,16{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(11\,B+39\,C\right)\,32{}\mathrm{i}}{693\,d}-\frac{B\,a\,16{}\mathrm{i}}{7\,d}+\frac{a\,\left(B+3\,C\right)\,32{}\mathrm{i}}{7\,d}\right)+\frac{a\,\left(3\,B+2\,C\right)\,16{}\mathrm{i}}{7\,d}+\frac{a\,\left(B-C\right)\,32{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(187\,B+168\,C\right)\,32{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(187\,B+168\,C\right)\,16{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(11*B - 42*C)*16i)/(1155*d) + (B*a*16i)/(5*d)) + (a*(3*B + 2*C)*16i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*a*256i)/(33*d) - (B*a*16i)/(9*d) + (a*(B + 2*C)*16i)/(3*d)) - (a*(3*B + 2*C)*16i)/(9*d) + (C*a*64i)/(9*d) + (a*(B + 4*C)*16i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*B + 2*C)*16i)/(11*d) - (a*(2*B + 3*C)*32i)/(11*d) + (B*a*16i)/(11*d)) - (a*(2*B + 3*C)*32i)/(11*d) + (a*(3*B + 2*C)*16i)/(11*d) + (B*a*16i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a*(3*B + 2*C)*16i)/(7*d) - exp(c*1i + d*x*1i)*((a*(11*B + 39*C)*32i)/(693*d) - (B*a*16i)/(7*d) + (a*(B + 3*C)*32i)/(7*d)) + (a*(B - C)*32i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(187*B + 168*C)*32i)/(3465*d*(exp(c*1i + d*x*1i) + 1)) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(187*B + 168*C)*16i)/(3465*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
366,1,596,189,11.396210,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a\,\left(3\,B+2\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{C\,a\,32{}\mathrm{i}}{63\,d}+\frac{a\,\left(B+4\,C\right)\,8{}\mathrm{i}}{7\,d}\right)+\frac{B\,a\,8{}\mathrm{i}}{7\,d}-\frac{C\,a\,32{}\mathrm{i}}{7\,d}-\frac{a\,\left(B+2\,C\right)\,24{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a\,\left(2\,B+3\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a\,\left(3\,B+2\,C\right)\,8{}\mathrm{i}}{9\,d}+\frac{B\,a\,8{}\mathrm{i}}{9\,d}\right)+\frac{a\,\left(2\,B+3\,C\right)\,16{}\mathrm{i}}{9\,d}-\frac{a\,\left(3\,B+2\,C\right)\,8{}\mathrm{i}}{9\,d}-\frac{B\,a\,8{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\left(\frac{B\,a\,8{}\mathrm{i}}{3\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(39\,B+34\,C\right)\,8{}\mathrm{i}}{315\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,B+2\,C\right)\,8{}\mathrm{i}}{5\,d}+\frac{a\,\left(3\,B+C\right)\,16{}\mathrm{i}}{105\,d}\right)-\frac{B\,a\,8{}\mathrm{i}}{5\,d}+\frac{a\,\left(B+3\,C\right)\,16{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(39\,B+34\,C\right)\,16{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*a*32i)/(63*d) - (a*(3*B + 2*C)*8i)/(7*d) + (a*(B + 4*C)*8i)/(7*d)) + (B*a*8i)/(7*d) - (C*a*32i)/(7*d) - (a*(B + 2*C)*24i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*B + 2*C)*8i)/(9*d) - (a*(2*B + 3*C)*16i)/(9*d) + (B*a*8i)/(9*d)) + (a*(2*B + 3*C)*16i)/(9*d) - (a*(3*B + 2*C)*8i)/(9*d) - (B*a*8i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + (((B*a*8i)/(3*d) - (a*exp(c*1i + d*x*1i)*(39*B + 34*C)*8i)/(315*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*B + 2*C)*8i)/(5*d) + (a*(3*B + C)*16i)/(105*d)) - (B*a*8i)/(5*d) + (a*(B + 3*C)*16i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(39*B + 34*C)*16i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
367,1,479,138,8.518880,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x),x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(7\,B+13\,C\right)\,8{}\mathrm{i}}{105\,d}-\frac{B\,a\,4{}\mathrm{i}}{3\,d}\right)-\frac{a\,\left(3\,B+2\,C\right)\,4{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a\,\left(2\,B+3\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(3\,B+2\,C\right)\,4{}\mathrm{i}}{7\,d}+\frac{B\,a\,4{}\mathrm{i}}{7\,d}\right)-\frac{a\,\left(2\,B+3\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(3\,B+2\,C\right)\,4{}\mathrm{i}}{7\,d}+\frac{B\,a\,4{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{B\,a\,4{}\mathrm{i}}{5\,d}+\frac{C\,a\,16{}\mathrm{i}}{35\,d}+\frac{a\,\left(B+2\,C\right)\,12{}\mathrm{i}}{5\,d}\right)-\frac{a\,\left(3\,B+2\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a\,\left(B+4\,C\right)\,4{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(63\,B+52\,C\right)\,4{}\mathrm{i}}{105\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*B + 2*C)*4i)/(7*d) - (a*(2*B + 3*C)*8i)/(7*d) + (B*a*4i)/(7*d)) - (a*(2*B + 3*C)*8i)/(7*d) + (a*(3*B + 2*C)*4i)/(7*d) + (B*a*4i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(7*B + 13*C)*8i)/(105*d) - (B*a*4i)/(3*d)) - (a*(3*B + 2*C)*4i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*a*16i)/(35*d) - (B*a*4i)/(5*d) + (a*(B + 2*C)*12i)/(5*d)) - (a*(3*B + 2*C)*4i)/(5*d) + (a*(B + 4*C)*4i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(63*B + 52*C)*4i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
368,1,213,101,7.581635,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","-\frac{2\,a\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}-1\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(B\,25{}\mathrm{i}+C\,18{}\mathrm{i}+B\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,10{}\mathrm{i}+B\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,50{}\mathrm{i}+B\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,10{}\mathrm{i}+B\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,25{}\mathrm{i}+C\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,18{}\mathrm{i}+C\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,48{}\mathrm{i}+C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,18{}\mathrm{i}+C\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,18{}\mathrm{i}\right)}{15\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"-(2*a*(exp(c*1i + d*x*1i) - 1)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(B*25i + C*18i + B*exp(c*1i + d*x*1i)*10i + B*exp(c*2i + d*x*2i)*50i + B*exp(c*3i + d*x*3i)*10i + B*exp(c*4i + d*x*4i)*25i + C*exp(c*1i + d*x*1i)*18i + C*exp(c*2i + d*x*2i)*48i + C*exp(c*3i + d*x*3i)*18i + C*exp(c*4i + d*x*4i)*18i))/(15*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
369,0,-1,105,0.000000,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
370,0,-1,103,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
371,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
372,0,-1,164,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
373,0,-1,209,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
374,1,988,282,14.046639,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{B\,a^2\,16{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(4\,B+5\,C\right)\,32{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(650\,B+811\,C\right)\,32{}\mathrm{i}}{9009\,d}\right)+\frac{C\,a^2\,32{}\mathrm{i}}{d}-\frac{a^2\,\left(5\,B+2\,C\right)\,16{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,16{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(403\,B+1046\,C\right)\,16{}\mathrm{i}}{15015\,d}\right)+\frac{a^2\,\left(5\,B+2\,C\right)\,16{}\mathrm{i}}{5\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,16{}\mathrm{i}}{3\,d}+\frac{a^2\,\left(9\,B+10\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(13\,B-6\,C\right)\,64{}\mathrm{i}}{1287\,d}\right)+\frac{a^2\,\left(B+6\,C\right)\,64{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,B+16\,C\right)\,16{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,16{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,80{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,16{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(11\,B+10\,C\right)\,16{}\mathrm{i}}{13\,d}\right)-\frac{B\,a^2\,16{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(3\,B+4\,C\right)\,80{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(5\,B+2\,C\right)\,16{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(11\,B+10\,C\right)\,16{}\mathrm{i}}{13\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^6}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,16{}\mathrm{i}}{11\,d}+\frac{C\,a^2\,1792{}\mathrm{i}}{143\,d}+\frac{a^2\,\left(B+2\,C\right)\,80{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(B+C\right)\,160{}\mathrm{i}}{11\,d}\right)-\frac{C\,a^2\,128{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(B-8\,C\right)\,16{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(5\,B+2\,C\right)\,16{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(5\,B+9\,C\right)\,32{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(4615\,B+4184\,C\right)\,32{}\mathrm{i}}{45045\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(4615\,B+4184\,C\right)\,16{}\mathrm{i}}{45045\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(4*B + 5*C)*32i)/(7*d) - (B*a^2*16i)/(7*d) + (a^2*(650*B + 811*C)*32i)/(9009*d)) + (C*a^2*32i)/d - (a^2*(5*B + 2*C)*16i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((exp(c*1i + d*x*1i)*((B*a^2*16i)/(5*d) - (a^2*(403*B + 1046*C)*16i)/(15015*d)) + (a^2*(5*B + 2*C)*16i)/(5*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*16i)/(3*d) + (a^2*(9*B + 10*C)*16i)/(9*d) + (a^2*(13*B - 6*C)*64i)/(1287*d)) + (a^2*(B + 6*C)*64i)/(9*d) - (a^2*(5*B + 2*C)*16i)/(9*d) + (a^2*(5*B + 16*C)*16i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*16i)/(13*d) + (a^2*(3*B + 4*C)*80i)/(13*d) - (a^2*(5*B + 2*C)*16i)/(13*d) - (a^2*(11*B + 10*C)*16i)/(13*d)) - (B*a^2*16i)/(13*d) - (a^2*(3*B + 4*C)*80i)/(13*d) + (a^2*(5*B + 2*C)*16i)/(13*d) + (a^2*(11*B + 10*C)*16i)/(13*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^6) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*16i)/(11*d) + (C*a^2*1792i)/(143*d) + (a^2*(B + 2*C)*80i)/(11*d) - (a^2*(B + C)*160i)/(11*d)) - (C*a^2*128i)/(11*d) + (a^2*(B - 8*C)*16i)/(11*d) + (a^2*(5*B + 2*C)*16i)/(11*d) - (a^2*(5*B + 9*C)*32i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(4615*B + 4184*C)*32i)/(45045*d*(exp(c*1i + d*x*1i) + 1)) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(4615*B + 4184*C)*16i)/(45045*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
375,1,855,237,15.401214,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{B\,a^2\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(803\,B+710\,C\right)\,8{}\mathrm{i}}{3465\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a^2\,\left(5\,B+2\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,B+16\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(11\,B+50\,C\right)\,32{}\mathrm{i}}{693\,d}\right)+\frac{B\,a^2\,24{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(9\,B+10\,C\right)\,8{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,40{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(11\,B+10\,C\right)\,8{}\mathrm{i}}{11\,d}\right)+\frac{B\,a^2\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,40{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(11\,B+10\,C\right)\,8{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{C\,a^2\,64{}\mathrm{i}}{99\,d}-\frac{a^2\,\left(B-8\,C\right)\,8{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,8{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,B+9\,C\right)\,16{}\mathrm{i}}{9\,d}\right)+\frac{B\,a^2\,8{}\mathrm{i}}{9\,d}+\frac{C\,a^2\,64{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(B+2\,C\right)\,40{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(B+C\right)\,80{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(5\,B+2\,C\right)\,8{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(44\,B-31\,C\right)\,16{}\mathrm{i}}{1155\,d}\right)-\frac{B\,a^2\,8{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(4\,B+5\,C\right)\,16{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(803\,B+710\,C\right)\,16{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((B*a^2*8i)/(3*d) - (a^2*exp(c*1i + d*x*1i)*(803*B + 710*C)*8i)/(3465*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((B*a^2*24i)/(7*d) - exp(c*1i + d*x*1i)*((a^2*(5*B + 16*C)*8i)/(7*d) - (a^2*(5*B + 2*C)*8i)/(7*d) + (a^2*(11*B + 50*C)*32i)/(693*d)) + (a^2*(9*B + 10*C)*8i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*8i)/(11*d) + (a^2*(3*B + 4*C)*40i)/(11*d) - (a^2*(5*B + 2*C)*8i)/(11*d) - (a^2*(11*B + 10*C)*8i)/(11*d)) + (B*a^2*8i)/(11*d) + (a^2*(3*B + 4*C)*40i)/(11*d) - (a^2*(5*B + 2*C)*8i)/(11*d) - (a^2*(11*B + 10*C)*8i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*a^2*64i)/(99*d) - (a^2*(B - 8*C)*8i)/(9*d) - (a^2*(5*B + 2*C)*8i)/(9*d) + (a^2*(5*B + 9*C)*16i)/(9*d)) + (B*a^2*8i)/(9*d) + (C*a^2*64i)/(9*d) + (a^2*(B + 2*C)*40i)/(9*d) - (a^2*(B + C)*80i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(5*B + 2*C)*8i)/(5*d) + (a^2*(44*B - 31*C)*16i)/(1155*d)) - (B*a^2*8i)/(5*d) + (a^2*(4*B + 5*C)*16i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(803*B + 710*C)*16i)/(3465*d*(exp(c*1i + d*x*1i) + 1))","B"
376,1,723,175,10.939983,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x),x)","\frac{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,4{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(60\,B+73\,C\right)\,8{}\mathrm{i}}{315\,d}\right)+\frac{a^2\,\left(5\,B+2\,C\right)\,4{}\mathrm{i}}{3\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{B\,a^2\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,16{}\mathrm{i}}{105\,d}+\frac{a^2\,\left(9\,B+10\,C\right)\,4{}\mathrm{i}}{5\,d}\right)-\frac{a^2\,\left(5\,B+2\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(5\,B+16\,C\right)\,4{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,4{}\mathrm{i}}{7\,d}+\frac{C\,a^2\,32{}\mathrm{i}}{63\,d}+\frac{a^2\,\left(B+2\,C\right)\,20{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(B+C\right)\,40{}\mathrm{i}}{7\,d}\right)+\frac{a^2\,\left(B-8\,C\right)\,4{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,B+2\,C\right)\,4{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,B+9\,C\right)\,8{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,20{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(11\,B+10\,C\right)\,4{}\mathrm{i}}{9\,d}\right)-\frac{B\,a^2\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(3\,B+4\,C\right)\,20{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,B+2\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(11\,B+10\,C\right)\,4{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(345\,B+292\,C\right)\,4{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((exp(c*1i + d*x*1i)*((B*a^2*4i)/(3*d) - (a^2*(60*B + 73*C)*8i)/(315*d)) + (a^2*(5*B + 2*C)*4i)/(3*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(3*B + 4*C)*16i)/(105*d) - (B*a^2*4i)/(5*d) + (a^2*(9*B + 10*C)*4i)/(5*d)) - (a^2*(5*B + 2*C)*4i)/(5*d) + (a^2*(5*B + 16*C)*4i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*4i)/(7*d) + (C*a^2*32i)/(63*d) + (a^2*(B + 2*C)*20i)/(7*d) - (a^2*(B + C)*40i)/(7*d)) + (a^2*(B - 8*C)*4i)/(7*d) + (a^2*(5*B + 2*C)*4i)/(7*d) - (a^2*(5*B + 9*C)*8i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*4i)/(9*d) + (a^2*(3*B + 4*C)*20i)/(9*d) - (a^2*(5*B + 2*C)*4i)/(9*d) - (a^2*(11*B + 10*C)*4i)/(9*d)) - (B*a^2*4i)/(9*d) - (a^2*(3*B + 4*C)*20i)/(9*d) + (a^2*(5*B + 2*C)*4i)/(9*d) + (a^2*(11*B + 10*C)*4i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(345*B + 292*C)*4i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
377,1,590,138,7.434869,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{B\,a^2\,2{}\mathrm{i}}{d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(301\,B+230\,C\right)\,2{}\mathrm{i}}{105\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,a^2\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(11\,B+10\,C\right)\,2{}\mathrm{i}}{7\,d}\right)+\frac{B\,a^2\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(3\,B+4\,C\right)\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,B+2\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(11\,B+10\,C\right)\,2{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(5\,B+2\,C\right)\,2{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(5\,B+9\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(7\,B-8\,C\right)\,2{}\mathrm{i}}{35\,d}\right)-\frac{B\,a^2\,2{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(B+2\,C\right)\,2{}\mathrm{i}}{d}+\frac{a^2\,\left(B+C\right)\,4{}\mathrm{i}}{d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(5\,B+2\,C\right)\,2{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(63\,B+80\,C\right)\,2{}\mathrm{i}}{105\,d}\right)-\frac{B\,a^2\,2{}\mathrm{i}}{3\,d}+\frac{a^2\,\left(9\,B+10\,C\right)\,2{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((B*a^2*2i)/d - (a^2*exp(c*1i + d*x*1i)*(301*B + 230*C)*2i)/(105*d)))/(exp(c*1i + d*x*1i) + 1) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((B*a^2*2i)/(7*d) + (a^2*(3*B + 4*C)*10i)/(7*d) - (a^2*(5*B + 2*C)*2i)/(7*d) - (a^2*(11*B + 10*C)*2i)/(7*d)) + (B*a^2*2i)/(7*d) + (a^2*(3*B + 4*C)*10i)/(7*d) - (a^2*(5*B + 2*C)*2i)/(7*d) - (a^2*(11*B + 10*C)*2i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(5*B + 2*C)*2i)/(5*d) - (a^2*(5*B + 9*C)*4i)/(5*d) + (a^2*(7*B - 8*C)*2i)/(35*d)) - (B*a^2*2i)/(5*d) - (a^2*(B + 2*C)*2i)/d + (a^2*(B + C)*4i)/d))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(5*B + 2*C)*2i)/(3*d) - (a^2*(63*B + 80*C)*2i)/(105*d)) - (B*a^2*2i)/(3*d) + (a^2*(9*B + 10*C)*2i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
378,0,-1,142,0.000000,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
379,0,-1,143,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
380,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
381,0,-1,164,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
382,0,-1,209,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
383,0,-1,254,0.000000,"\text{Not used}","int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^6\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
384,0,-1,243,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)), x)","F"
385,0,-1,202,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)), x)","F"
386,0,-1,159,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)), x)","F"
387,0,-1,118,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)), x)","F"
388,0,-1,78,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/2), x)","F"
389,0,-1,91,0.000000,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
390,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
391,0,-1,165,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
392,0,-1,206,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
393,0,-1,261,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)), x)","F"
394,0,-1,216,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)), x)","F"
395,0,-1,171,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)), x)","F"
396,0,-1,118,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)), x)","F"
397,0,-1,87,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(3/2), x)","F"
398,0,-1,127,0.000000,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
399,0,-1,170,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
400,0,-1,221,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
401,0,-1,261,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)), x)","F"
402,0,-1,216,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)), x)","F"
403,0,-1,169,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)), x)","F"
404,0,-1,126,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)), x)","F"
405,0,-1,126,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/2), x)","F"
406,0,-1,164,0.000000,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
407,0,-1,207,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
408,1,251,152,6.559388,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,B+3\,C\right)}{2\,\left(2\,A\,a+\frac{3\,B\,a}{2}+\frac{3\,C\,a}{2}\right)}\right)\,\left(4\,A+3\,B+3\,C\right)}{4\,d}-\frac{\left(A\,a+\frac{3\,B\,a}{4}+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{10\,A\,a}{3}-\frac{29\,B\,a}{6}-\frac{13\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,a}{3}+\frac{20\,B\,a}{3}+\frac{116\,C\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{22\,A\,a}{3}-\frac{35\,B\,a}{6}-\frac{19\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,B\,a}{4}+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh((a*tan(c/2 + (d*x)/2)*(4*A + 3*B + 3*C))/(2*(2*A*a + (3*B*a)/2 + (3*C*a)/2)))*(4*A + 3*B + 3*C))/(4*d) - (tan(c/2 + (d*x)/2)*(3*A*a + (13*B*a)/4 + (13*C*a)/4) + tan(c/2 + (d*x)/2)^9*(A*a + (3*B*a)/4 + (3*C*a)/4) - tan(c/2 + (d*x)/2)^7*((10*A*a)/3 + (29*B*a)/6 + (13*C*a)/6) - tan(c/2 + (d*x)/2)^3*((22*A*a)/3 + (35*B*a)/6 + (19*C*a)/6) + tan(c/2 + (d*x)/2)^5*((20*A*a)/3 + (20*B*a)/3 + (116*C*a)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
409,1,211,127,6.535742,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\left(-A\,a-B\,a-\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(5\,A\,a+\frac{7\,B\,a}{3}+\frac{49\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-7\,A\,a-\frac{13\,B\,a}{3}-\frac{31\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+3\,B\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+4\,B+3\,C\right)}{2\,\left(2\,A\,a+2\,B\,a+\frac{3\,C\,a}{2}\right)}\right)\,\left(4\,A+4\,B+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + 3*B*a + (13*C*a)/4) - tan(c/2 + (d*x)/2)^7*(A*a + B*a + (3*C*a)/4) - tan(c/2 + (d*x)/2)^3*(7*A*a + (13*B*a)/3 + (31*C*a)/12) + tan(c/2 + (d*x)/2)^5*(5*A*a + (7*B*a)/3 + (49*C*a)/12))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh((a*tan(c/2 + (d*x)/2)*(4*A + 4*B + 3*C))/(2*(2*A*a + 2*B*a + (3*C*a)/2)))*(4*A + 4*B + 3*C))/(4*d)","B"
410,1,165,92,5.801758,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{a\,\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A+B+C\right)}{4\,A\,a+2\,B\,a+2\,C\,a}\right)\,\left(2\,A+B+C\right)}{d}-\frac{\left(2\,A\,a+B\,a+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a-4\,B\,a-\frac{4\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+3\,B\,a+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh((2*a*tan(c/2 + (d*x)/2)*(2*A + B + C))/(4*A*a + 2*B*a + 2*C*a))*(2*A + B + C))/d - (tan(c/2 + (d*x)/2)*(2*A*a + 3*B*a + 3*C*a) + tan(c/2 + (d*x)/2)^5*(2*A*a + B*a + C*a) - tan(c/2 + (d*x)/2)^3*(4*A*a + 4*B*a + (4*C*a)/3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
411,1,176,63,3.508597,"\text{Not used}","int((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{C\,a\,\sin\left(c+d\,x\right)}{2}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(-A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}+B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}+\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2}\right)}{d}","Not used",1,"((C*a*sin(c + d*x))/2 + (B*a*sin(2*c + 2*d*x))/2 + (C*a*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*(A*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i - A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i + (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2))/d","B"
412,1,159,46,3.383573,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{C\,a\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}-\frac{B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(C*a*tan(c + d*x))/d + (2*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (A*a*sin(2*c + 2*d*x))/(2*d*cos(c + d*x))","B"
413,1,159,62,3.379140,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(A*a*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (A*a*sin(2*c + 2*d*x))/(4*d)","B"
414,1,100,82,3.080500,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{A\,a\,x}{2}+\frac{B\,a\,x}{2}+C\,a\,x+\frac{3\,A\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*a*x)/2 + (B*a*x)/2 + C*a*x + (3*A*a*sin(c + d*x))/(4*d) + (B*a*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (A*a*sin(2*c + 2*d*x))/(4*d) + (A*a*sin(3*c + 3*d*x))/(12*d) + (B*a*sin(2*c + 2*d*x))/(4*d)","B"
415,1,209,102,5.546402,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{3\,A\,a}{4}+B\,a+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{49\,A\,a}{12}+\frac{7\,B\,a}{3}+5\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{31\,A\,a}{12}+\frac{13\,B\,a}{3}+7\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,B\,a+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,B+4\,C\right)}{4\,\left(\frac{3\,A\,a}{4}+B\,a+C\,a\right)}\right)\,\left(3\,A+4\,B+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*B*a + 3*C*a) + tan(c/2 + (d*x)/2)^7*((3*A*a)/4 + B*a + C*a) + tan(c/2 + (d*x)/2)^3*((31*A*a)/12 + (13*B*a)/3 + 7*C*a) + tan(c/2 + (d*x)/2)^5*((49*A*a)/12 + (7*B*a)/3 + 5*C*a))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(3*A + 4*B + 4*C))/(4*((3*A*a)/4 + B*a + C*a)))*(3*A + 4*B + 4*C))/(4*d)","B"
416,1,248,141,5.700822,"\text{Not used}","int(cos(c + d*x)^5*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{13\,A\,a}{6}+\frac{29\,B\,a}{6}+\frac{10\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,B\,a}{3}+\frac{20\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{19\,A\,a}{6}+\frac{35\,B\,a}{6}+\frac{22\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+\frac{13\,B\,a}{4}+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+3\,B+4\,C\right)}{4\,\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}+C\,a\right)}\right)\,\left(3\,A+3\,B+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + (13*B*a)/4 + 3*C*a) + tan(c/2 + (d*x)/2)^9*((3*A*a)/4 + (3*B*a)/4 + C*a) + tan(c/2 + (d*x)/2)^7*((13*A*a)/6 + (29*B*a)/6 + (10*C*a)/3) + tan(c/2 + (d*x)/2)^3*((19*A*a)/6 + (35*B*a)/6 + (22*C*a)/3) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*B*a)/3 + (20*C*a)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(3*A + 3*B + 4*C))/(4*((3*A*a)/4 + (3*B*a)/4 + C*a)))*(3*A + 3*B + 4*C))/(4*d)","B"
417,1,337,222,6.591301,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{a^2\,\mathrm{atanh}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(14\,A+12\,B+11\,C\right)}{4\,\left(\frac{7\,A\,a^2}{2}+3\,B\,a^2+\frac{11\,C\,a^2}{4}\right)}\right)\,\left(14\,A+12\,B+11\,C\right)}{8\,d}-\frac{\left(\frac{7\,A\,a^2}{4}+\frac{3\,B\,a^2}{2}+\frac{11\,C\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-\frac{119\,A\,a^2}{12}-\frac{17\,B\,a^2}{2}-\frac{187\,C\,a^2}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{43\,A\,a^2}{2}+\frac{107\,B\,a^2}{5}+\frac{331\,C\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{53\,A\,a^2}{2}-\frac{117\,B\,a^2}{5}-\frac{501\,C\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{233\,A\,a^2}{12}+\frac{31\,B\,a^2}{2}+\frac{87\,C\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{25\,A\,a^2}{4}-\frac{13\,B\,a^2}{2}-\frac{53\,C\,a^2}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^2*atanh((a^2*tan(c/2 + (d*x)/2)*(14*A + 12*B + 11*C))/(4*((7*A*a^2)/2 + 3*B*a^2 + (11*C*a^2)/4)))*(14*A + 12*B + 11*C))/(8*d) - (tan(c/2 + (d*x)/2)^11*((7*A*a^2)/4 + (3*B*a^2)/2 + (11*C*a^2)/8) - tan(c/2 + (d*x)/2)^9*((119*A*a^2)/12 + (17*B*a^2)/2 + (187*C*a^2)/24) + tan(c/2 + (d*x)/2)^3*((233*A*a^2)/12 + (31*B*a^2)/2 + (87*C*a^2)/8) + tan(c/2 + (d*x)/2)^7*((43*A*a^2)/2 + (107*B*a^2)/5 + (331*C*a^2)/20) - tan(c/2 + (d*x)/2)^5*((53*A*a^2)/2 + (117*B*a^2)/5 + (501*C*a^2)/20) - tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + (13*B*a^2)/2 + (53*C*a^2)/8))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
418,1,286,190,3.932840,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(A+\frac{7\,B}{8}+\frac{3\,C}{4}\right)}{d}-\frac{\left(2\,A\,a^2+\frac{7\,B\,a^2}{4}+\frac{3\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{28\,A\,a^2}{3}-\frac{49\,B\,a^2}{6}-7\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{56\,A\,a^2}{3}+\frac{40\,B\,a^2}{3}+\frac{72\,C\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{52\,A\,a^2}{3}-\frac{79\,B\,a^2}{6}-9\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A\,a^2+\frac{25\,B\,a^2}{4}+\frac{13\,C\,a^2}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(8\,A+7\,B+6\,C\right)}{8\,d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2) + 1)*(A + (7*B)/8 + (3*C)/4))/d - (tan(c/2 + (d*x)/2)^9*(2*A*a^2 + (7*B*a^2)/4 + (3*C*a^2)/2) - tan(c/2 + (d*x)/2)^7*((28*A*a^2)/3 + (49*B*a^2)/6 + 7*C*a^2) - tan(c/2 + (d*x)/2)^3*((52*A*a^2)/3 + (79*B*a^2)/6 + 9*C*a^2) + tan(c/2 + (d*x)/2)^5*((56*A*a^2)/3 + (40*B*a^2)/3 + (72*C*a^2)/5) + tan(c/2 + (d*x)/2)*(6*A*a^2 + (25*B*a^2)/4 + (13*C*a^2)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - (a^2*log(tan(c/2 + (d*x)/2) - 1)*(8*A + 7*B + 6*C))/(8*d)","B"
419,1,245,147,6.508669,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{2\,a^2\,\mathrm{atanh}\left(\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A}{2}+B+\frac{7\,C}{8}\right)}{6\,A\,a^2+4\,B\,a^2+\frac{7\,C\,a^2}{2}}\right)\,\left(\frac{3\,A}{2}+B+\frac{7\,C}{8}\right)}{d}-\frac{\left(3\,A\,a^2+2\,B\,a^2+\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-11\,A\,a^2-\frac{22\,B\,a^2}{3}-\frac{77\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(13\,A\,a^2+\frac{34\,B\,a^2}{3}+\frac{83\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-5\,A\,a^2-6\,B\,a^2-\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(2*a^2*atanh((4*a^2*tan(c/2 + (d*x)/2)*((3*A)/2 + B + (7*C)/8))/(6*A*a^2 + 4*B*a^2 + (7*C*a^2)/2))*((3*A)/2 + B + (7*C)/8))/d - (tan(c/2 + (d*x)/2)^7*(3*A*a^2 + 2*B*a^2 + (7*C*a^2)/4) - tan(c/2 + (d*x)/2)^5*(11*A*a^2 + (22*B*a^2)/3 + (77*C*a^2)/12) + tan(c/2 + (d*x)/2)^3*(13*A*a^2 + (34*B*a^2)/3 + (83*C*a^2)/12) - tan(c/2 + (d*x)/2)*(5*A*a^2 + 6*B*a^2 + (25*C*a^2)/4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
420,1,421,120,4.110211,"\text{Not used}","int((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{2}+\frac{3\,C\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,A\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+3\,A\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{9\,B\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{3\,C\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+\frac{3\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*a^2*sin(3*c + 3*d*x))/4 + (B*a^2*sin(2*c + 2*d*x))/4 + (B*a^2*sin(3*c + 3*d*x))/2 + (C*a^2*sin(2*c + 2*d*x))/2 + (5*C*a^2*sin(3*c + 3*d*x))/12 + (A*a^2*sin(c + d*x))/4 + (B*a^2*sin(c + d*x))/2 + (3*C*a^2*sin(c + d*x))/4 + (3*A*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 3*A*a^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (9*B*a^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (3*C*a^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + (3*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
421,1,244,121,3.830509,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+C\,a^2\,\sin\left(2\,c+2\,d\,x\right)+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(-2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}-B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}\right)}{d}","Not used",1,"((A*a^2*sin(3*c + 3*d*x))/4 + (B*a^2*sin(2*c + 2*d*x))/2 + C*a^2*sin(2*c + 2*d*x) + (A*a^2*sin(c + d*x))/4 + (C*a^2*sin(c + d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*(A*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i - 2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + (C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2))/d","B"
422,1,232,128,3.550087,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{3\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+4\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}+2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{8}+C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(3*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 4*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (A*a^2*sin(2*c + 2*d*x) + (A*a^2*sin(3*c + 3*d*x))/8 + (B*a^2*sin(2*c + 2*d*x))/2 + (A*a^2*sin(c + d*x))/8 + C*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
423,1,223,134,3.359901,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{7\,A\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(7*A*a^2*sin(c + d*x))/(4*d) + (2*B*a^2*sin(c + d*x))/d + (C*a^2*sin(c + d*x))/d + (2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^2*sin(2*c + 2*d*x))/(2*d) + (A*a^2*sin(3*c + 3*d*x))/(12*d) + (B*a^2*sin(2*c + 2*d*x))/(4*d)","B"
424,1,174,149,3.100729,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{7\,A\,a^2\,x}{8}+B\,a^2\,x+\frac{3\,C\,a^2\,x}{2}+\frac{3\,A\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{7\,B\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{A\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(7*A*a^2*x)/8 + B*a^2*x + (3*C*a^2*x)/2 + (3*A*a^2*sin(c + d*x))/(2*d) + (7*B*a^2*sin(c + d*x))/(4*d) + (2*C*a^2*sin(c + d*x))/d + (A*a^2*sin(2*c + 2*d*x))/(2*d) + (A*a^2*sin(3*c + 3*d*x))/(6*d) + (A*a^2*sin(4*c + 4*d*x))/(32*d) + (B*a^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*sin(3*c + 3*d*x))/(12*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d)","B"
425,1,289,187,5.954820,"\text{Not used}","int(cos(c + d*x)^5*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{3\,A\,a^2}{2}+\frac{7\,B\,a^2}{4}+2\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(7\,A\,a^2+\frac{49\,B\,a^2}{6}+\frac{28\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{72\,A\,a^2}{5}+\frac{40\,B\,a^2}{3}+\frac{56\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(9\,A\,a^2+\frac{79\,B\,a^2}{6}+\frac{52\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a^2}{2}+\frac{25\,B\,a^2}{4}+6\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,A+7\,B+8\,C\right)}{4\,\left(\frac{3\,A\,a^2}{2}+\frac{7\,B\,a^2}{4}+2\,C\,a^2\right)}\right)\,\left(6\,A+7\,B+8\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*((3*A*a^2)/2 + (7*B*a^2)/4 + 2*C*a^2) + tan(c/2 + (d*x)/2)^7*(7*A*a^2 + (49*B*a^2)/6 + (28*C*a^2)/3) + tan(c/2 + (d*x)/2)^3*(9*A*a^2 + (79*B*a^2)/6 + (52*C*a^2)/3) + tan(c/2 + (d*x)/2)^5*((72*A*a^2)/5 + (40*B*a^2)/3 + (56*C*a^2)/3) + tan(c/2 + (d*x)/2)*((13*A*a^2)/2 + (25*B*a^2)/4 + 6*C*a^2))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(6*A + 7*B + 8*C))/(4*((3*A*a^2)/2 + (7*B*a^2)/4 + 2*C*a^2)))*(6*A + 7*B + 8*C))/(4*d)","B"
426,1,333,213,5.855669,"\text{Not used}","int(cos(c + d*x)^6*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{11\,A\,a^2}{8}+\frac{3\,B\,a^2}{2}+\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{187\,A\,a^2}{24}+\frac{17\,B\,a^2}{2}+\frac{119\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{331\,A\,a^2}{20}+\frac{107\,B\,a^2}{5}+\frac{43\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{501\,A\,a^2}{20}+\frac{117\,B\,a^2}{5}+\frac{53\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{87\,A\,a^2}{8}+\frac{31\,B\,a^2}{2}+\frac{233\,C\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{53\,A\,a^2}{8}+\frac{13\,B\,a^2}{2}+\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,A+12\,B+14\,C\right)}{8\,\left(\frac{11\,A\,a^2}{8}+\frac{3\,B\,a^2}{2}+\frac{7\,C\,a^2}{4}\right)}\right)\,\left(11\,A+12\,B+14\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((11*A*a^2)/8 + (3*B*a^2)/2 + (7*C*a^2)/4) + tan(c/2 + (d*x)/2)^9*((187*A*a^2)/24 + (17*B*a^2)/2 + (119*C*a^2)/12) + tan(c/2 + (d*x)/2)^3*((87*A*a^2)/8 + (31*B*a^2)/2 + (233*C*a^2)/12) + tan(c/2 + (d*x)/2)^7*((331*A*a^2)/20 + (107*B*a^2)/5 + (43*C*a^2)/2) + tan(c/2 + (d*x)/2)^5*((501*A*a^2)/20 + (117*B*a^2)/5 + (53*C*a^2)/2) + tan(c/2 + (d*x)/2)*((53*A*a^2)/8 + (13*B*a^2)/2 + (25*C*a^2)/4))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(11*A + 12*B + 14*C))/(8*((11*A*a^2)/8 + (3*B*a^2)/2 + (7*C*a^2)/4)))*(11*A + 12*B + 14*C))/(8*d)","B"
427,1,381,274,6.791204,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{a^3\,\mathrm{atanh}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(26\,A+23\,B+21\,C\right)}{4\,\left(\frac{13\,A\,a^3}{2}+\frac{23\,B\,a^3}{4}+\frac{21\,C\,a^3}{4}\right)}\right)\,\left(26\,A+23\,B+21\,C\right)}{8\,d}-\frac{\left(\frac{13\,A\,a^3}{4}+\frac{23\,B\,a^3}{8}+\frac{21\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(-\frac{65\,A\,a^3}{3}-\frac{115\,B\,a^3}{6}-\frac{35\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3679\,A\,a^3}{60}+\frac{6509\,B\,a^3}{120}+\frac{1981\,C\,a^3}{40}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{464\,A\,a^3}{5}-\frac{432\,B\,a^3}{5}-\frac{2608\,C\,a^3}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{5089\,A\,a^3}{60}+\frac{2993\,B\,a^3}{40}+\frac{3011\,C\,a^3}{40}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{143\,A\,a^3}{3}-\frac{79\,B\,a^3}{2}-\frac{61\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+\frac{105\,B\,a^3}{8}+\frac{107\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh((a^3*tan(c/2 + (d*x)/2)*(26*A + 23*B + 21*C))/(4*((13*A*a^3)/2 + (23*B*a^3)/4 + (21*C*a^3)/4)))*(26*A + 23*B + 21*C))/(8*d) - (tan(c/2 + (d*x)/2)^13*((13*A*a^3)/4 + (23*B*a^3)/8 + (21*C*a^3)/8) - tan(c/2 + (d*x)/2)^11*((65*A*a^3)/3 + (115*B*a^3)/6 + (35*C*a^3)/2) - tan(c/2 + (d*x)/2)^3*((143*A*a^3)/3 + (79*B*a^3)/2 + (61*C*a^3)/2) - tan(c/2 + (d*x)/2)^7*((464*A*a^3)/5 + (432*B*a^3)/5 + (2608*C*a^3)/35) + tan(c/2 + (d*x)/2)^5*((5089*A*a^3)/60 + (2993*B*a^3)/40 + (3011*C*a^3)/40) + tan(c/2 + (d*x)/2)^9*((3679*A*a^3)/60 + (6509*B*a^3)/120 + (1981*C*a^3)/40) + tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (105*B*a^3)/8 + (107*C*a^3)/8))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
428,1,337,216,6.519615,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{a^3\,\mathrm{atanh}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(30\,A+26\,B+23\,C\right)}{4\,\left(\frac{15\,A\,a^3}{2}+\frac{13\,B\,a^3}{2}+\frac{23\,C\,a^3}{4}\right)}\right)\,\left(30\,A+26\,B+23\,C\right)}{8\,d}-\frac{\left(\frac{15\,A\,a^3}{4}+\frac{13\,B\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-\frac{85\,A\,a^3}{4}-\frac{221\,B\,a^3}{12}-\frac{391\,C\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{99\,A\,a^3}{2}+\frac{429\,B\,a^3}{10}+\frac{759\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{125\,A\,a^3}{2}-\frac{499\,B\,a^3}{10}-\frac{969\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{171\,A\,a^3}{4}+\frac{419\,B\,a^3}{12}+\frac{211\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{49\,A\,a^3}{4}-\frac{51\,B\,a^3}{4}-\frac{105\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*atanh((a^3*tan(c/2 + (d*x)/2)*(30*A + 26*B + 23*C))/(4*((15*A*a^3)/2 + (13*B*a^3)/2 + (23*C*a^3)/4)))*(30*A + 26*B + 23*C))/(8*d) - (tan(c/2 + (d*x)/2)^11*((15*A*a^3)/4 + (13*B*a^3)/4 + (23*C*a^3)/8) - tan(c/2 + (d*x)/2)^9*((85*A*a^3)/4 + (221*B*a^3)/12 + (391*C*a^3)/24) + tan(c/2 + (d*x)/2)^3*((171*A*a^3)/4 + (419*B*a^3)/12 + (211*C*a^3)/8) + tan(c/2 + (d*x)/2)^7*((99*A*a^3)/2 + (429*B*a^3)/10 + (759*C*a^3)/20) - tan(c/2 + (d*x)/2)^5*((125*A*a^3)/2 + (499*B*a^3)/10 + (969*C*a^3)/20) - tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + (51*B*a^3)/4 + (105*C*a^3)/8))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
429,1,292,175,6.562539,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{a^3\,\mathrm{atanh}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,A+15\,B+13\,C\right)}{2\,\left(10\,A\,a^3+\frac{15\,B\,a^3}{2}+\frac{13\,C\,a^3}{2}\right)}\right)\,\left(20\,A+15\,B+13\,C\right)}{4\,d}-\frac{\left(5\,A\,a^3+\frac{15\,B\,a^3}{4}+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{70\,A\,a^3}{3}-\frac{35\,B\,a^3}{2}-\frac{91\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{128\,A\,a^3}{3}+32\,B\,a^3+\frac{416\,C\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{106\,A\,a^3}{3}-\frac{61\,B\,a^3}{2}-\frac{133\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A\,a^3+\frac{49\,B\,a^3}{4}+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh((a^3*tan(c/2 + (d*x)/2)*(20*A + 15*B + 13*C))/(2*(10*A*a^3 + (15*B*a^3)/2 + (13*C*a^3)/2)))*(20*A + 15*B + 13*C))/(4*d) - (tan(c/2 + (d*x)/2)^9*(5*A*a^3 + (15*B*a^3)/4 + (13*C*a^3)/4) - tan(c/2 + (d*x)/2)^7*((70*A*a^3)/3 + (35*B*a^3)/2 + (91*C*a^3)/6) - tan(c/2 + (d*x)/2)^3*((106*A*a^3)/3 + (61*B*a^3)/2 + (133*C*a^3)/6) + tan(c/2 + (d*x)/2)^5*((128*A*a^3)/3 + 32*B*a^3 + (416*C*a^3)/15) + tan(c/2 + (d*x)/2)*(11*A*a^3 + (49*B*a^3)/4 + (51*C*a^3)/4))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
430,1,611,162,4.910642,"\text{Not used}","int((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{9\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{63\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{45\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{135\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+9\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{9\,A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{2}+13\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)+\frac{9\,B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{11\,B\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{2}+15\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)+\frac{45\,C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{9\,C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{2}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{9\,B\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{69\,C\,a^3\,\sin\left(c+d\,x\right)}{8}+12\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+3\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+42\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{21\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{2}+30\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{15\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{2}+\frac{45\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{45\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}}{12\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"(9*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (63*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (45*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (135*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + 9*A*a^3*sin(2*c + 2*d*x) + (3*A*a^3*sin(3*c + 3*d*x))/2 + (9*A*a^3*sin(4*c + 4*d*x))/2 + 13*B*a^3*sin(2*c + 2*d*x) + (9*B*a^3*sin(3*c + 3*d*x))/2 + (11*B*a^3*sin(4*c + 4*d*x))/2 + 15*C*a^3*sin(2*c + 2*d*x) + (45*C*a^3*sin(3*c + 3*d*x))/8 + (9*C*a^3*sin(4*c + 4*d*x))/2 + (3*A*a^3*sin(c + d*x))/2 + (9*B*a^3*sin(c + d*x))/2 + (69*C*a^3*sin(c + d*x))/8 + 12*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 3*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 42*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (21*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 + 30*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (15*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 + (45*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (45*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8)/(12*d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
431,1,523,156,4.436623,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{11\,C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{5\,C\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{9\,A\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{9\,A\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{3\,B\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{21\,B\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{15\,C\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{3\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{7\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{5\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*a^3*sin(2*c + 2*d*x))/4 + (A*a^3*sin(3*c + 3*d*x))/4 + (A*a^3*sin(4*c + 4*d*x))/8 + (B*a^3*sin(2*c + 2*d*x))/4 + (3*B*a^3*sin(3*c + 3*d*x))/4 + (3*C*a^3*sin(2*c + 2*d*x))/4 + (11*C*a^3*sin(3*c + 3*d*x))/12 + (A*a^3*sin(c + d*x))/4 + (3*B*a^3*sin(c + d*x))/4 + (5*C*a^3*sin(c + d*x))/4 + (9*A*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (9*A*a^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (3*B*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (21*B*a^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (15*C*a^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (3*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (3*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (7*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (5*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
432,1,329,171,4.095787,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(\frac{7\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}+3\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}+C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,7{}\mathrm{i}}{2}\right)}{d}+\frac{\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{3\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((7*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i + 3*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i + C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*7i)/2))/d + ((A*a^3*sin(2*c + 2*d*x))/8 + (3*A*a^3*sin(3*c + 3*d*x))/4 + (A*a^3*sin(4*c + 4*d*x))/16 + (B*a^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(3*c + 3*d*x))/4 + (3*C*a^3*sin(2*c + 2*d*x))/2 + (3*A*a^3*sin(c + d*x))/4 + (B*a^3*sin(c + d*x))/4 + (C*a^3*sin(c + d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
433,1,290,169,3.803343,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{5\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+7\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}+6\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}+\frac{\frac{23\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{3\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{24}+\frac{3\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{8}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{8}+C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(5*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 7*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 6*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/d + ((23*A*a^3*sin(2*c + 2*d*x))/12 + (3*A*a^3*sin(3*c + 3*d*x))/8 + (A*a^3*sin(4*c + 4*d*x))/24 + (3*B*a^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(3*c + 3*d*x))/8 + (C*a^3*sin(2*c + 2*d*x))/2 + (3*A*a^3*sin(c + d*x))/8 + (B*a^3*sin(c + d*x))/8 + C*a^3*sin(c + d*x))/(d*cos(c + d*x))","B"
434,1,243,183,3.711061,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{45\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+60\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+84\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+24\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+12\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)+3\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)+\frac{3\,A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+9\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)+B\,a^3\,\sin\left(3\,c+3\,d\,x\right)+3\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)+39\,A\,a^3\,\sin\left(c+d\,x\right)+45\,B\,a^3\,\sin\left(c+d\,x\right)+36\,C\,a^3\,\sin\left(c+d\,x\right)}{12\,d}","Not used",1,"(45*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 60*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 84*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 24*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 12*A*a^3*sin(2*c + 2*d*x) + 3*A*a^3*sin(3*c + 3*d*x) + (3*A*a^3*sin(4*c + 4*d*x))/8 + 9*B*a^3*sin(2*c + 2*d*x) + B*a^3*sin(3*c + 3*d*x) + 3*C*a^3*sin(2*c + 2*d*x) + 39*A*a^3*sin(c + d*x) + 45*B*a^3*sin(c + d*x) + 36*C*a^3*sin(c + d*x))/(12*d)","B"
435,1,289,179,5.882188,"\text{Not used}","int(cos(c + d*x)^5*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{13\,A\,a^3}{4}+\frac{15\,B\,a^3}{4}+5\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{91\,A\,a^3}{6}+\frac{35\,B\,a^3}{2}+\frac{70\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,A\,a^3}{15}+32\,B\,a^3+\frac{128\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{133\,A\,a^3}{6}+\frac{61\,B\,a^3}{2}+\frac{106\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+\frac{49\,B\,a^3}{4}+11\,C\,a^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,A+15\,B+20\,C\right)}{4\,\left(\frac{13\,A\,a^3}{4}+\frac{15\,B\,a^3}{4}+5\,C\,a^3\right)}\right)\,\left(13\,A+15\,B+20\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*((13*A*a^3)/4 + (15*B*a^3)/4 + 5*C*a^3) + tan(c/2 + (d*x)/2)^7*((91*A*a^3)/6 + (35*B*a^3)/2 + (70*C*a^3)/3) + tan(c/2 + (d*x)/2)^3*((133*A*a^3)/6 + (61*B*a^3)/2 + (106*C*a^3)/3) + tan(c/2 + (d*x)/2)^5*((416*A*a^3)/15 + 32*B*a^3 + (128*C*a^3)/3) + tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (49*B*a^3)/4 + 11*C*a^3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(13*A + 15*B + 20*C))/(4*((13*A*a^3)/4 + (15*B*a^3)/4 + 5*C*a^3)))*(13*A + 15*B + 20*C))/(4*d)","B"
436,1,333,235,5.780312,"\text{Not used}","int(cos(c + d*x)^6*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{23\,A\,a^3}{8}+\frac{13\,B\,a^3}{4}+\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{391\,A\,a^3}{24}+\frac{221\,B\,a^3}{12}+\frac{85\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{759\,A\,a^3}{20}+\frac{429\,B\,a^3}{10}+\frac{99\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{969\,A\,a^3}{20}+\frac{499\,B\,a^3}{10}+\frac{125\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{211\,A\,a^3}{8}+\frac{419\,B\,a^3}{12}+\frac{171\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{105\,A\,a^3}{8}+\frac{51\,B\,a^3}{4}+\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,A+26\,B+30\,C\right)}{8\,\left(\frac{23\,A\,a^3}{8}+\frac{13\,B\,a^3}{4}+\frac{15\,C\,a^3}{4}\right)}\right)\,\left(23\,A+26\,B+30\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((23*A*a^3)/8 + (13*B*a^3)/4 + (15*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((391*A*a^3)/24 + (221*B*a^3)/12 + (85*C*a^3)/4) + tan(c/2 + (d*x)/2)^3*((211*A*a^3)/8 + (419*B*a^3)/12 + (171*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((759*A*a^3)/20 + (429*B*a^3)/10 + (99*C*a^3)/2) + tan(c/2 + (d*x)/2)^5*((969*A*a^3)/20 + (499*B*a^3)/10 + (125*C*a^3)/2) + tan(c/2 + (d*x)/2)*((105*A*a^3)/8 + (51*B*a^3)/4 + (49*C*a^3)/4))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(23*A + 26*B + 30*C))/(8*((23*A*a^3)/8 + (13*B*a^3)/4 + (15*C*a^3)/4)))*(23*A + 26*B + 30*C))/(8*d)","B"
437,1,377,265,6.067596,"\text{Not used}","int(cos(c + d*x)^7*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{21\,A\,a^3}{8}+\frac{23\,B\,a^3}{8}+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{35\,A\,a^3}{2}+\frac{115\,B\,a^3}{6}+\frac{65\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1981\,A\,a^3}{40}+\frac{6509\,B\,a^3}{120}+\frac{3679\,C\,a^3}{60}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{2608\,A\,a^3}{35}+\frac{432\,B\,a^3}{5}+\frac{464\,C\,a^3}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3011\,A\,a^3}{40}+\frac{2993\,B\,a^3}{40}+\frac{5089\,C\,a^3}{60}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{61\,A\,a^3}{2}+\frac{79\,B\,a^3}{2}+\frac{143\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{107\,A\,a^3}{8}+\frac{105\,B\,a^3}{8}+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(21\,A+23\,B+26\,C\right)}{8\,\left(\frac{21\,A\,a^3}{8}+\frac{23\,B\,a^3}{8}+\frac{13\,C\,a^3}{4}\right)}\right)\,\left(21\,A+23\,B+26\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^13*((21*A*a^3)/8 + (23*B*a^3)/8 + (13*C*a^3)/4) + tan(c/2 + (d*x)/2)^11*((35*A*a^3)/2 + (115*B*a^3)/6 + (65*C*a^3)/3) + tan(c/2 + (d*x)/2)^3*((61*A*a^3)/2 + (79*B*a^3)/2 + (143*C*a^3)/3) + tan(c/2 + (d*x)/2)^7*((2608*A*a^3)/35 + (432*B*a^3)/5 + (464*C*a^3)/5) + tan(c/2 + (d*x)/2)^5*((3011*A*a^3)/40 + (2993*B*a^3)/40 + (5089*C*a^3)/60) + tan(c/2 + (d*x)/2)^9*((1981*A*a^3)/40 + (6509*B*a^3)/120 + (3679*C*a^3)/60) + tan(c/2 + (d*x)/2)*((107*A*a^3)/8 + (105*B*a^3)/8 + (51*C*a^3)/4))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(21*A + 23*B + 26*C))/(8*((21*A*a^3)/8 + (23*B*a^3)/8 + (13*C*a^3)/4)))*(21*A + 23*B + 26*C))/(8*d)","B"
438,1,381,252,6.648581,"\text{Not used}","int(((a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{a^4\,\mathrm{atanh}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56\,A+49\,B+44\,C\right)}{4\,\left(14\,A\,a^4+\frac{49\,B\,a^4}{4}+11\,C\,a^4\right)}\right)\,\left(56\,A+49\,B+44\,C\right)}{8\,d}-\frac{\left(7\,A\,a^4+\frac{49\,B\,a^4}{8}+\frac{11\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(-\frac{140\,A\,a^4}{3}-\frac{245\,B\,a^4}{6}-\frac{110\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1981\,A\,a^4}{15}+\frac{13867\,B\,a^4}{120}+\frac{3113\,C\,a^4}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{1024\,A\,a^4}{5}-\frac{896\,B\,a^4}{5}-\frac{5632\,C\,a^4}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{2851\,A\,a^4}{15}+\frac{19157\,B\,a^4}{120}+\frac{1501\,C\,a^4}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{308\,A\,a^4}{3}-\frac{523\,B\,a^4}{6}-70\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{207\,B\,a^4}{8}+\frac{53\,C\,a^4}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^4*atanh((a^4*tan(c/2 + (d*x)/2)*(56*A + 49*B + 44*C))/(4*(14*A*a^4 + (49*B*a^4)/4 + 11*C*a^4)))*(56*A + 49*B + 44*C))/(8*d) - (tan(c/2 + (d*x)/2)^13*(7*A*a^4 + (49*B*a^4)/8 + (11*C*a^4)/2) - tan(c/2 + (d*x)/2)^11*((140*A*a^4)/3 + (245*B*a^4)/6 + (110*C*a^4)/3) - tan(c/2 + (d*x)/2)^3*((308*A*a^4)/3 + (523*B*a^4)/6 + 70*C*a^4) - tan(c/2 + (d*x)/2)^7*((1024*A*a^4)/5 + (896*B*a^4)/5 + (5632*C*a^4)/35) + tan(c/2 + (d*x)/2)^9*((1981*A*a^4)/15 + (13867*B*a^4)/120 + (3113*C*a^4)/30) + tan(c/2 + (d*x)/2)^5*((2851*A*a^4)/15 + (19157*B*a^4)/120 + (1501*C*a^4)/10) + tan(c/2 + (d*x)/2)*(25*A*a^4 + (207*B*a^4)/8 + (53*C*a^4)/2))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
439,1,338,209,6.562518,"\text{Not used}","int(((a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{7\,a^4\,\mathrm{atanh}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,A+8\,B+7\,C\right)}{4\,\left(\frac{35\,A\,a^4}{2}+14\,B\,a^4+\frac{49\,C\,a^4}{4}\right)}\right)\,\left(10\,A+8\,B+7\,C\right)}{8\,d}-\frac{\left(\frac{35\,A\,a^4}{4}+7\,B\,a^4+\frac{49\,C\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-\frac{595\,A\,a^4}{12}-\frac{119\,B\,a^4}{3}-\frac{833\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{231\,A\,a^4}{2}+\frac{462\,B\,a^4}{5}+\frac{1617\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{281\,A\,a^4}{2}-\frac{562\,B\,a^4}{5}-\frac{1967\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{1069\,A\,a^4}{12}+\frac{233\,B\,a^4}{3}+\frac{1471\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{93\,A\,a^4}{4}-25\,B\,a^4-\frac{207\,C\,a^4}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(7*a^4*atanh((7*a^4*tan(c/2 + (d*x)/2)*(10*A + 8*B + 7*C))/(4*((35*A*a^4)/2 + 14*B*a^4 + (49*C*a^4)/4)))*(10*A + 8*B + 7*C))/(8*d) - (tan(c/2 + (d*x)/2)^11*((35*A*a^4)/4 + 7*B*a^4 + (49*C*a^4)/8) - tan(c/2 + (d*x)/2)^9*((595*A*a^4)/12 + (119*B*a^4)/3 + (833*C*a^4)/24) + tan(c/2 + (d*x)/2)^7*((231*A*a^4)/2 + (462*B*a^4)/5 + (1617*C*a^4)/20) + tan(c/2 + (d*x)/2)^3*((1069*A*a^4)/12 + (233*B*a^4)/3 + (1471*C*a^4)/24) - tan(c/2 + (d*x)/2)^5*((281*A*a^4)/2 + (562*B*a^4)/5 + (1967*C*a^4)/20) - tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + 25*B*a^4 + (207*C*a^4)/8))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
440,1,996,195,4.748430,"\text{Not used}","int((a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{30\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+80\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)+15\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)+25\,A\,a^4\,\sin\left(5\,c+5\,d\,x\right)+\frac{465\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+95\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{405\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+25\,B\,a^4\,\sin\left(5\,c+5\,d\,x\right)+\frac{165\,C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{385\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{105\,C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{83\,C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{4}+55\,A\,a^4\,\sin\left(c+d\,x\right)+70\,B\,a^4\,\sin\left(c+d\,x\right)+\frac{175\,C\,a^4\,\sin\left(c+d\,x\right)}{2}+\frac{75\,A\,a^4\,\mathrm{atan}\left(\frac{2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+2688\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+1960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+784\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2368\,A^2+3360\,A\,B+2688\,A\,C+1225\,B^2+1960\,B\,C+784\,C^2\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{15\,A\,a^4\,\mathrm{atan}\left(\frac{2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+2688\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+1960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+784\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2368\,A^2+3360\,A\,B+2688\,A\,C+1225\,B^2+1960\,B\,C+784\,C^2\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{2}+450\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{2625\,B\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{525\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+225\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+45\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)+\frac{2625\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{525\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{16}+\frac{525\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{105\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}+75\,A\,a^4\,\mathrm{atan}\left(\frac{2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+2688\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+1960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+784\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2368\,A^2+3360\,A\,B+2688\,A\,C+1225\,B^2+1960\,B\,C+784\,C^2\right)}\right)\,\cos\left(c+d\,x\right)}{60\,d\,\left(\frac{5\,\cos\left(c+d\,x\right)}{8}+\frac{5\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{\cos\left(5\,c+5\,d\,x\right)}{16}\right)}","Not used",1,"(30*A*a^4*sin(2*c + 2*d*x) + 80*A*a^4*sin(3*c + 3*d*x) + 15*A*a^4*sin(4*c + 4*d*x) + 25*A*a^4*sin(5*c + 5*d*x) + (465*B*a^4*sin(2*c + 2*d*x))/8 + 95*B*a^4*sin(3*c + 3*d*x) + (405*B*a^4*sin(4*c + 4*d*x))/16 + 25*B*a^4*sin(5*c + 5*d*x) + (165*C*a^4*sin(2*c + 2*d*x))/2 + (385*C*a^4*sin(3*c + 3*d*x))/4 + (105*C*a^4*sin(4*c + 4*d*x))/4 + (83*C*a^4*sin(5*c + 5*d*x))/4 + 55*A*a^4*sin(c + d*x) + 70*B*a^4*sin(c + d*x) + (175*C*a^4*sin(c + d*x))/2 + (75*A*a^4*atan((2368*A^2*sin(c/2 + (d*x)/2) + 1225*B^2*sin(c/2 + (d*x)/2) + 784*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 2688*A*C*sin(c/2 + (d*x)/2) + 1960*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(2368*A^2 + 1225*B^2 + 784*C^2 + 3360*A*B + 2688*A*C + 1960*B*C)))*cos(3*c + 3*d*x))/2 + (15*A*a^4*atan((2368*A^2*sin(c/2 + (d*x)/2) + 1225*B^2*sin(c/2 + (d*x)/2) + 784*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 2688*A*C*sin(c/2 + (d*x)/2) + 1960*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(2368*A^2 + 1225*B^2 + 784*C^2 + 3360*A*B + 2688*A*C + 1960*B*C)))*cos(5*c + 5*d*x))/2 + 450*A*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (2625*B*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (525*C*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 225*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + 45*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x) + (2625*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/16 + (525*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/16 + (525*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (105*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4 + 75*A*a^4*atan((2368*A^2*sin(c/2 + (d*x)/2) + 1225*B^2*sin(c/2 + (d*x)/2) + 784*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 2688*A*C*sin(c/2 + (d*x)/2) + 1960*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(2368*A^2 + 1225*B^2 + 784*C^2 + 3360*A*B + 2688*A*C + 1960*B*C)))*cos(c + d*x))/(60*d*((5*cos(c + d*x))/8 + (5*cos(3*c + 3*d*x))/16 + cos(5*c + 5*d*x)/16))","B"
441,1,1346,196,4.843790,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{117\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+54\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{315\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+12\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{15\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+6\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)+\frac{3\,A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{4}+22\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)+6\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)+28\,C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{81\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+10\,C\,a^4\,\sin\left(4\,c+4\,d\,x\right)+36\,A\,a^4\,\mathrm{atan}\left(\frac{3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3728\,A^2+5504\,A\,B+3640\,A\,C+2368\,B^2+3360\,B\,C+1225\,C^2\right)}\right)+9\,B\,a^4\,\mathrm{atan}\left(\frac{3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3728\,A^2+5504\,A\,B+3640\,A\,C+2368\,B^2+3360\,B\,C+1225\,C^2\right)}\right)+3\,A\,a^4\,\sin\left(c+d\,x\right)+6\,B\,a^4\,\sin\left(c+d\,x\right)+\frac{105\,C\,a^4\,\sin\left(c+d\,x\right)}{8}+48\,A\,a^4\,\mathrm{atan}\left(\frac{3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3728\,A^2+5504\,A\,B+3640\,A\,C+2368\,B^2+3360\,B\,C+1225\,C^2\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+12\,A\,a^4\,\mathrm{atan}\left(\frac{3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3728\,A^2+5504\,A\,B+3640\,A\,C+2368\,B^2+3360\,B\,C+1225\,C^2\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+12\,B\,a^4\,\mathrm{atan}\left(\frac{3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3728\,A^2+5504\,A\,B+3640\,A\,C+2368\,B^2+3360\,B\,C+1225\,C^2\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+3\,B\,a^4\,\mathrm{atan}\left(\frac{3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3728\,A^2+5504\,A\,B+3640\,A\,C+2368\,B^2+3360\,B\,C+1225\,C^2\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+78\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{39\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{2}+72\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+18\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+\frac{105\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{105\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}}{12\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((117*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 54*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (315*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + 12*A*a^4*sin(2*c + 2*d*x) + (15*A*a^4*sin(3*c + 3*d*x))/4 + 6*A*a^4*sin(4*c + 4*d*x) + (3*A*a^4*sin(5*c + 5*d*x))/4 + 22*B*a^4*sin(2*c + 2*d*x) + 6*B*a^4*sin(3*c + 3*d*x) + 10*B*a^4*sin(4*c + 4*d*x) + 28*C*a^4*sin(2*c + 2*d*x) + (81*C*a^4*sin(3*c + 3*d*x))/8 + 10*C*a^4*sin(4*c + 4*d*x) + 36*A*a^4*atan((3728*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 1225*C^2*sin(c/2 + (d*x)/2) + 5504*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(3728*A^2 + 2368*B^2 + 1225*C^2 + 5504*A*B + 3640*A*C + 3360*B*C))) + 9*B*a^4*atan((3728*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 1225*C^2*sin(c/2 + (d*x)/2) + 5504*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(3728*A^2 + 2368*B^2 + 1225*C^2 + 5504*A*B + 3640*A*C + 3360*B*C))) + 3*A*a^4*sin(c + d*x) + 6*B*a^4*sin(c + d*x) + (105*C*a^4*sin(c + d*x))/8 + 48*A*a^4*atan((3728*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 1225*C^2*sin(c/2 + (d*x)/2) + 5504*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(3728*A^2 + 2368*B^2 + 1225*C^2 + 5504*A*B + 3640*A*C + 3360*B*C)))*cos(2*c + 2*d*x) + 12*A*a^4*atan((3728*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 1225*C^2*sin(c/2 + (d*x)/2) + 5504*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(3728*A^2 + 2368*B^2 + 1225*C^2 + 5504*A*B + 3640*A*C + 3360*B*C)))*cos(4*c + 4*d*x) + 12*B*a^4*atan((3728*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 1225*C^2*sin(c/2 + (d*x)/2) + 5504*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(3728*A^2 + 2368*B^2 + 1225*C^2 + 5504*A*B + 3640*A*C + 3360*B*C)))*cos(2*c + 2*d*x) + 3*B*a^4*atan((3728*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 1225*C^2*sin(c/2 + (d*x)/2) + 5504*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(3728*A^2 + 2368*B^2 + 1225*C^2 + 5504*A*B + 3640*A*C + 3360*B*C)))*cos(4*c + 4*d*x) + 78*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (39*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 + 72*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 18*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + (105*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (105*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8)/(12*d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
442,1,625,209,5.056563,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{3\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{33\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{3\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{2}+\frac{3\,A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{32}+\frac{3\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+3\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{3\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+3\,C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+5\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{15\,A\,a^4\,\sin\left(c+d\,x\right)}{16}+3\,B\,a^4\,\sin\left(c+d\,x\right)+6\,C\,a^4\,\sin\left(c+d\,x\right)+\frac{117\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+18\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+18\,B\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{117\,B\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{9\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+27\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{39\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+6\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+6\,B\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+\frac{39\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+9\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{3\,d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"(3*A*a^4*sin(2*c + 2*d*x) + (33*A*a^4*sin(3*c + 3*d*x))/32 + (3*A*a^4*sin(4*c + 4*d*x))/2 + (3*A*a^4*sin(5*c + 5*d*x))/32 + (3*B*a^4*sin(2*c + 2*d*x))/2 + 3*B*a^4*sin(3*c + 3*d*x) + (3*B*a^4*sin(4*c + 4*d*x))/8 + 3*C*a^4*sin(2*c + 2*d*x) + 5*C*a^4*sin(3*c + 3*d*x) + (15*A*a^4*sin(c + d*x))/16 + 3*B*a^4*sin(c + d*x) + 6*C*a^4*sin(c + d*x) + (117*A*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + 18*A*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 18*B*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (117*B*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (9*C*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 27*C*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (39*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + 6*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + 6*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + (39*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (3*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + 9*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/(3*d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
443,1,373,217,4.531743,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(6\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}+\frac{13\,B\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-B\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}+4\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,13{}\mathrm{i}}{2}\right)}{d}+\frac{\frac{A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{83\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48}+\frac{A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{48}+\frac{5\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+2\,C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{41\,A\,a^4\,\sin\left(c+d\,x\right)}{24}+B\,a^4\,\sin\left(c+d\,x\right)+\frac{3\,C\,a^4\,\sin\left(c+d\,x\right)}{4}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(6*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - A*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i + (13*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - B*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i + 4*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (C*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*13i)/2))/d + ((A*a^4*sin(2*c + 2*d*x))/2 + (83*A*a^4*sin(3*c + 3*d*x))/48 + (A*a^4*sin(4*c + 4*d*x))/4 + (A*a^4*sin(5*c + 5*d*x))/48 + (5*B*a^4*sin(2*c + 2*d*x))/8 + B*a^4*sin(3*c + 3*d*x) + (B*a^4*sin(4*c + 4*d*x))/16 + 2*C*a^4*sin(2*c + 2*d*x) + (C*a^4*sin(3*c + 3*d*x))/4 + (41*A*a^4*sin(c + d*x))/24 + B*a^4*sin(c + d*x) + (3*C*a^4*sin(c + d*x))/4)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
444,1,1244,217,4.603695,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","-\frac{\left(\frac{35\,A\,a^4}{4}+10\,B\,a^4+5\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{70\,A\,a^4}{3}+\frac{76\,B\,a^4}{3}+8\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{21\,A\,a^4}{2}+8\,B\,a^4-10\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{58\,A\,a^4}{3}-\frac{76\,B\,a^4}{3}-24\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{93\,A\,a^4}{4}-18\,B\,a^4-11\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)-\frac{a^4\,\left(35\,A+48\,B+52\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(35\,A+48\,B+52\,C\right)}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)+\frac{a^4\,\left(35\,A+48\,B+52\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(35\,A+48\,B+52\,C\right)}{8}}{1920\,B^3\,a^{12}+4160\,C^3\,a^{12}+3080\,A\,B^2\,a^{12}+1225\,A^2\,B\,a^{12}+10080\,A\,C^2\,a^{12}+4900\,A^2\,C\,a^{12}+13200\,B\,C^2\,a^{12}+10720\,B^2\,C\,a^{12}+14840\,A\,B\,C\,a^{12}-\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)-\frac{a^4\,\left(35\,A+48\,B+52\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(35\,A+48\,B+52\,C\right)\,1{}\mathrm{i}}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)+\frac{a^4\,\left(35\,A+48\,B+52\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(35\,A+48\,B+52\,C\right)\,1{}\mathrm{i}}{8}}\right)\,\left(35\,A+48\,B+52\,C\right)}{4\,d}-\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)+a^4\,\left(B+4\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\right)\,\left(B+4\,C\right)\,1{}\mathrm{i}+a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)-a^4\,\left(B+4\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\right)\,\left(B+4\,C\right)\,1{}\mathrm{i}}{1920\,B^3\,a^{12}+4160\,C^3\,a^{12}+3080\,A\,B^2\,a^{12}+1225\,A^2\,B\,a^{12}+10080\,A\,C^2\,a^{12}+4900\,A^2\,C\,a^{12}+13200\,B\,C^2\,a^{12}+10720\,B^2\,C\,a^{12}+a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)+a^4\,\left(B+4\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\right)\,\left(B+4\,C\right)-a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1225\,A^2\,a^8}{2}+1680\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+2752\,B\,C\,a^8+1864\,C^2\,a^8\right)-a^4\,\left(B+4\,C\right)\,\left(140\,A\,a^4+224\,B\,a^4+336\,C\,a^4\right)\right)\,\left(B+4\,C\right)+14840\,A\,B\,C\,a^{12}}\right)\,\left(B+4\,C\right)\,2{}\mathrm{i}}{d}","Not used",1,"- (tan(c/2 + (d*x)/2)^5*((21*A*a^4)/2 + 8*B*a^4 - 10*C*a^4) + tan(c/2 + (d*x)/2)^9*((35*A*a^4)/4 + 10*B*a^4 + 5*C*a^4) - tan(c/2 + (d*x)/2)^3*((58*A*a^4)/3 + (76*B*a^4)/3 + 24*C*a^4) + tan(c/2 + (d*x)/2)^7*((70*A*a^4)/3 + (76*B*a^4)/3 + 8*C*a^4) - tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + 18*B*a^4 + 11*C*a^4))/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1)) - (a^4*atan(((a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) - (a^4*(35*A + 48*B + 52*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4)*1i)/8)*(35*A + 48*B + 52*C))/8 + (a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) + (a^4*(35*A + 48*B + 52*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4)*1i)/8)*(35*A + 48*B + 52*C))/8)/(1920*B^3*a^12 + 4160*C^3*a^12 + 3080*A*B^2*a^12 + 1225*A^2*B*a^12 + 10080*A*C^2*a^12 + 4900*A^2*C*a^12 + 13200*B*C^2*a^12 + 10720*B^2*C*a^12 - (a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) - (a^4*(35*A + 48*B + 52*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4)*1i)/8)*(35*A + 48*B + 52*C)*1i)/8 + (a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) + (a^4*(35*A + 48*B + 52*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4)*1i)/8)*(35*A + 48*B + 52*C)*1i)/8 + 14840*A*B*C*a^12))*(35*A + 48*B + 52*C))/(4*d) - (a^4*atan((a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) + a^4*(B + 4*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4))*(B + 4*C)*1i + a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) - a^4*(B + 4*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4))*(B + 4*C)*1i)/(1920*B^3*a^12 + 4160*C^3*a^12 + 3080*A*B^2*a^12 + 1225*A^2*B*a^12 + 10080*A*C^2*a^12 + 4900*A^2*C*a^12 + 13200*B*C^2*a^12 + 10720*B^2*C*a^12 + a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) + a^4*(B + 4*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4))*(B + 4*C) - a^4*(tan(c/2 + (d*x)/2)*((1225*A^2*a^8)/2 + 1184*B^2*a^8 + 1864*C^2*a^8 + 1680*A*B*a^8 + 1820*A*C*a^8 + 2752*B*C*a^8) - a^4*(B + 4*C)*(140*A*a^4 + 224*B*a^4 + 336*C*a^4))*(B + 4*C) + 14840*A*B*C*a^12))*(B + 4*C)*2i)/d","B"
445,1,1151,225,4.454550,"\text{Not used}","int(cos(c + d*x)^5*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(7\,A\,a^4+\frac{35\,B\,a^4}{4}+10\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{98\,A\,a^4}{3}+\frac{245\,B\,a^4}{6}+\frac{136\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{896\,A\,a^4}{15}+\frac{224\,B\,a^4}{3}+\frac{236\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{158\,A\,a^4}{3}+\frac{395\,B\,a^4}{6}+\frac{184\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{93\,B\,a^4}{4}+18\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{C\,a^4\,\mathrm{atan}\left(\frac{C\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)+C\,a^4\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\right)\,1{}\mathrm{i}+C\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)-C\,a^4\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\right)\,1{}\mathrm{i}}{1920\,C^3\,a^{12}+2464\,A\,C^2\,a^{12}+784\,A^2\,C\,a^{12}+3080\,B\,C^2\,a^{12}+1225\,B^2\,C\,a^{12}+C\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)+C\,a^4\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\right)-C\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)-C\,a^4\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\right)+1960\,A\,B\,C\,a^{12}}\right)\,2{}\mathrm{i}}{d}-\frac{a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)-\frac{a^4\,\left(28\,A+35\,B+48\,C\right)\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(28\,A+35\,B+48\,C\right)}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)+\frac{a^4\,\left(28\,A+35\,B+48\,C\right)\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(28\,A+35\,B+48\,C\right)}{8}}{1920\,C^3\,a^{12}+2464\,A\,C^2\,a^{12}+784\,A^2\,C\,a^{12}+3080\,B\,C^2\,a^{12}+1225\,B^2\,C\,a^{12}+1960\,A\,B\,C\,a^{12}-\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)-\frac{a^4\,\left(28\,A+35\,B+48\,C\right)\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(28\,A+35\,B+48\,C\right)\,1{}\mathrm{i}}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A^2\,a^8+980\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+1680\,B\,C\,a^8+1184\,C^2\,a^8\right)+\frac{a^4\,\left(28\,A+35\,B+48\,C\right)\,\left(112\,A\,a^4+140\,B\,a^4+224\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(28\,A+35\,B+48\,C\right)\,1{}\mathrm{i}}{8}}\right)\,\left(28\,A+35\,B+48\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(7*A*a^4 + (35*B*a^4)/4 + 10*C*a^4) + tan(c/2 + (d*x)/2)^7*((98*A*a^4)/3 + (245*B*a^4)/6 + (136*C*a^4)/3) + tan(c/2 + (d*x)/2)^3*((158*A*a^4)/3 + (395*B*a^4)/6 + (184*C*a^4)/3) + tan(c/2 + (d*x)/2)^5*((896*A*a^4)/15 + (224*B*a^4)/3 + (236*C*a^4)/3) + tan(c/2 + (d*x)/2)*(25*A*a^4 + (93*B*a^4)/4 + 18*C*a^4))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (C*a^4*atan((C*a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) + C*a^4*(112*A*a^4 + 140*B*a^4 + 224*C*a^4))*1i + C*a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) - C*a^4*(112*A*a^4 + 140*B*a^4 + 224*C*a^4))*1i)/(1920*C^3*a^12 + 2464*A*C^2*a^12 + 784*A^2*C*a^12 + 3080*B*C^2*a^12 + 1225*B^2*C*a^12 + C*a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) + C*a^4*(112*A*a^4 + 140*B*a^4 + 224*C*a^4)) - C*a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) - C*a^4*(112*A*a^4 + 140*B*a^4 + 224*C*a^4)) + 1960*A*B*C*a^12))*2i)/d - (a^4*atan(((a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) - (a^4*(28*A + 35*B + 48*C)*(112*A*a^4 + 140*B*a^4 + 224*C*a^4)*1i)/8)*(28*A + 35*B + 48*C))/8 + (a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) + (a^4*(28*A + 35*B + 48*C)*(112*A*a^4 + 140*B*a^4 + 224*C*a^4)*1i)/8)*(28*A + 35*B + 48*C))/8)/(1920*C^3*a^12 + 2464*A*C^2*a^12 + 784*A^2*C*a^12 + 3080*B*C^2*a^12 + 1225*B^2*C*a^12 - (a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) - (a^4*(28*A + 35*B + 48*C)*(112*A*a^4 + 140*B*a^4 + 224*C*a^4)*1i)/8)*(28*A + 35*B + 48*C)*1i)/8 + (a^4*(tan(c/2 + (d*x)/2)*(392*A^2*a^8 + (1225*B^2*a^8)/2 + 1184*C^2*a^8 + 980*A*B*a^8 + 1344*A*C*a^8 + 1680*B*C*a^8) + (a^4*(28*A + 35*B + 48*C)*(112*A*a^4 + 140*B*a^4 + 224*C*a^4)*1i)/8)*(28*A + 35*B + 48*C)*1i)/8 + 1960*A*B*C*a^12))*(28*A + 35*B + 48*C))/(4*d)","B"
446,1,334,213,5.688803,"\text{Not used}","int(cos(c + d*x)^6*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{49\,A\,a^4}{8}+7\,B\,a^4+\frac{35\,C\,a^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{833\,A\,a^4}{24}+\frac{119\,B\,a^4}{3}+\frac{595\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{1617\,A\,a^4}{20}+\frac{462\,B\,a^4}{5}+\frac{231\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1967\,A\,a^4}{20}+\frac{562\,B\,a^4}{5}+\frac{281\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{1471\,A\,a^4}{24}+\frac{233\,B\,a^4}{3}+\frac{1069\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+25\,B\,a^4+\frac{93\,C\,a^4}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{7\,a^4\,\mathrm{atan}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,A+8\,B+10\,C\right)}{8\,\left(\frac{49\,A\,a^4}{8}+7\,B\,a^4+\frac{35\,C\,a^4}{4}\right)}\right)\,\left(7\,A+8\,B+10\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((49*A*a^4)/8 + 7*B*a^4 + (35*C*a^4)/4) + tan(c/2 + (d*x)/2)^9*((833*A*a^4)/24 + (119*B*a^4)/3 + (595*C*a^4)/12) + tan(c/2 + (d*x)/2)^7*((1617*A*a^4)/20 + (462*B*a^4)/5 + (231*C*a^4)/2) + tan(c/2 + (d*x)/2)^3*((1471*A*a^4)/24 + (233*B*a^4)/3 + (1069*C*a^4)/12) + tan(c/2 + (d*x)/2)^5*((1967*A*a^4)/20 + (562*B*a^4)/5 + (281*C*a^4)/2) + tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + 25*B*a^4 + (93*C*a^4)/4))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (7*a^4*atan((7*a^4*tan(c/2 + (d*x)/2)*(7*A + 8*B + 10*C))/(8*((49*A*a^4)/8 + 7*B*a^4 + (35*C*a^4)/4)))*(7*A + 8*B + 10*C))/(8*d)","B"
447,1,377,278,5.881542,"\text{Not used}","int(cos(c + d*x)^7*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{11\,A\,a^4}{2}+\frac{49\,B\,a^4}{8}+7\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{110\,A\,a^4}{3}+\frac{245\,B\,a^4}{6}+\frac{140\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3113\,A\,a^4}{30}+\frac{13867\,B\,a^4}{120}+\frac{1981\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{5632\,A\,a^4}{35}+\frac{896\,B\,a^4}{5}+\frac{1024\,C\,a^4}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1501\,A\,a^4}{10}+\frac{19157\,B\,a^4}{120}+\frac{2851\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(70\,A\,a^4+\frac{523\,B\,a^4}{6}+\frac{308\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{53\,A\,a^4}{2}+\frac{207\,B\,a^4}{8}+25\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(44\,A+49\,B+56\,C\right)}{8\,\left(\frac{11\,A\,a^4}{2}+\frac{49\,B\,a^4}{8}+7\,C\,a^4\right)}\right)\,\left(44\,A+49\,B+56\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^13*((11*A*a^4)/2 + (49*B*a^4)/8 + 7*C*a^4) + tan(c/2 + (d*x)/2)^11*((110*A*a^4)/3 + (245*B*a^4)/6 + (140*C*a^4)/3) + tan(c/2 + (d*x)/2)^3*(70*A*a^4 + (523*B*a^4)/6 + (308*C*a^4)/3) + tan(c/2 + (d*x)/2)^7*((5632*A*a^4)/35 + (896*B*a^4)/5 + (1024*C*a^4)/5) + tan(c/2 + (d*x)/2)^9*((3113*A*a^4)/30 + (13867*B*a^4)/120 + (1981*C*a^4)/15) + tan(c/2 + (d*x)/2)^5*((1501*A*a^4)/10 + (19157*B*a^4)/120 + (2851*C*a^4)/15) + tan(c/2 + (d*x)/2)*((53*A*a^4)/2 + (207*B*a^4)/8 + 25*C*a^4))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(44*A + 49*B + 56*C))/(8*((11*A*a^4)/2 + (49*B*a^4)/8 + 7*C*a^4)))*(44*A + 49*B + 56*C))/(8*d)","B"
448,1,421,303,5.976441,"\text{Not used}","int(cos(c + d*x)^8*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{323\,A\,a^4}{64}+\frac{11\,B\,a^4}{2}+\frac{49\,C\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+\left(\frac{7429\,A\,a^4}{192}+\frac{253\,B\,a^4}{6}+\frac{1127\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{123709\,A\,a^4}{960}+\frac{4213\,B\,a^4}{30}+\frac{18767\,C\,a^4}{120}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1632119\,A\,a^4}{6720}+\frac{55583\,B\,a^4}{210}+\frac{35371\,C\,a^4}{120}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{624003\,A\,a^4}{2240}+\frac{21771\,B\,a^4}{70}+\frac{40661\,C\,a^4}{120}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{68673\,A\,a^4}{320}+\frac{2201\,B\,a^4}{10}+\frac{29617\,C\,a^4}{120}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5033\,A\,a^4}{64}+\frac{193\,B\,a^4}{2}+\frac{2713\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{1725\,A\,a^4}{64}+\frac{53\,B\,a^4}{2}+\frac{207\,C\,a^4}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(323\,A+352\,B+392\,C\right)}{64\,\left(\frac{323\,A\,a^4}{64}+\frac{11\,B\,a^4}{2}+\frac{49\,C\,a^4}{8}\right)}\right)\,\left(323\,A+352\,B+392\,C\right)}{64\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^15*((323*A*a^4)/64 + (11*B*a^4)/2 + (49*C*a^4)/8) + tan(c/2 + (d*x)/2)^3*((5033*A*a^4)/64 + (193*B*a^4)/2 + (2713*C*a^4)/24) + tan(c/2 + (d*x)/2)^13*((7429*A*a^4)/192 + (253*B*a^4)/6 + (1127*C*a^4)/24) + tan(c/2 + (d*x)/2)^5*((68673*A*a^4)/320 + (2201*B*a^4)/10 + (29617*C*a^4)/120) + tan(c/2 + (d*x)/2)^11*((123709*A*a^4)/960 + (4213*B*a^4)/30 + (18767*C*a^4)/120) + tan(c/2 + (d*x)/2)^7*((624003*A*a^4)/2240 + (21771*B*a^4)/70 + (40661*C*a^4)/120) + tan(c/2 + (d*x)/2)^9*((1632119*A*a^4)/6720 + (55583*B*a^4)/210 + (35371*C*a^4)/120) + tan(c/2 + (d*x)/2)*((1725*A*a^4)/64 + (53*B*a^4)/2 + (207*C*a^4)/8))/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(323*A + 352*B + 392*C))/(64*((323*A*a^4)/64 + (11*B*a^4)/2 + (49*C*a^4)/8)))*(323*A + 352*B + 392*C))/(64*d)","B"
449,1,203,183,4.286695,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A-4\,B+5\,C\right)}{4\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}-\frac{\left(5\,B-3\,A-\frac{25\,C}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(7\,A-\frac{31\,B}{3}+\frac{115\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{25\,B}{3}-5\,A-\frac{109\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A-3\,B+\frac{7\,C}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2))*(4*A - 4*B + 5*C))/(4*a*d) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) - (tan(c/2 + (d*x)/2)*(A - 3*B + (7*C)/4) - tan(c/2 + (d*x)/2)^7*(3*A - 5*B + (25*C)/4) - tan(c/2 + (d*x)/2)^3*(5*A - (25*B)/3 + (109*C)/12) + tan(c/2 + (d*x)/2)^5*(7*A - (31*B)/3 + (115*C)/12))/(d*(a - 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 - 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8))","B"
450,1,165,148,3.809284,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))),x)","\frac{\left(2\,A-3\,B+5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,B-4\,A-\frac{16\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-B+3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-\frac{3\,B}{2}+\frac{3\,C}{2}\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A - B + 3*C) + tan(c/2 + (d*x)/2)^5*(2*A - 3*B + 5*C) - tan(c/2 + (d*x)/2)^3*(4*A - 4*B + (16*C)/3))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6)) + (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) - (2*atanh(tan(c/2 + (d*x)/2))*(A - (3*B)/2 + (3*C)/2))/(a*d)","B"
451,1,124,119,3.434637,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-B+\frac{3\,C}{2}\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-3\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-C\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A - B + (3*C)/2))/(a*d) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) - (tan(c/2 + (d*x)/2)^3*(2*B - 3*C) - tan(c/2 + (d*x)/2)*(2*B - C))/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4))","B"
452,1,79,63,3.348495,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) + (2*C*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) + (2*atanh(tan(c/2 + (d*x)/2))*(B - C))/(a*d)","B"
453,1,113,52,3.418733,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x)),x)","\frac{2\,A\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(2*A*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) - (A*sin(c/2 + (d*x)/2) - B*sin(c/2 + (d*x)/2) + C*sin(c/2 + (d*x)/2))/(a*d*cos(c/2 + (d*x)/2))","B"
454,1,66,62,3.281253,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}-\frac{x\,\left(A-B\right)}{a}+\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) - (x*(A - B))/a + (2*A*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2))","B"
455,1,111,108,3.572440,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{x\,\left(3\,A-2\,B+2\,C\right)}{2\,a}-\frac{\left(3\,A-2\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A-2\,B\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}","Not used",1,"(x*(3*A - 2*B + 2*C))/(2*a) - (tan(c/2 + (d*x)/2)^3*(3*A - 2*B) + tan(c/2 + (d*x)/2)*(A - 2*B))/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d)","B"
456,1,153,139,4.742452,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{\left(5\,A-3\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,A}{3}-4\,B+4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{x\,\left(3\,A-3\,B+2\,C\right)}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A - B + 2*C) + tan(c/2 + (d*x)/2)^5*(5*A - 3*B + 2*C) + tan(c/2 + (d*x)/2)^3*((16*A)/3 - 4*B + 4*C))/(d*(a + 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6)) - (x*(3*A - 3*B + 2*C))/(2*a) + (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d)","B"
457,1,189,174,5.245790,"\text{Not used}","int((cos(c + d*x)^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\frac{3\,x\,\left(5\,A-4\,B+4\,C\right)}{8\,a}-\frac{\left(\frac{25\,A}{4}-5\,B+3\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{115\,A}{12}-\frac{31\,B}{3}+7\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{109\,A}{12}-\frac{25\,B}{3}+5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{7\,A}{4}-3\,B+C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}","Not used",1,"(3*x*(5*A - 4*B + 4*C))/(8*a) - (tan(c/2 + (d*x)/2)*((7*A)/4 - 3*B + C) + tan(c/2 + (d*x)/2)^7*((25*A)/4 - 5*B + 3*C) + tan(c/2 + (d*x)/2)^3*((109*A)/12 - (25*B)/3 + 5*C) + tan(c/2 + (d*x)/2)^5*((115*A)/12 - (31*B)/3 + 7*C))/(d*(a + 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 + 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8)) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d)","B"
458,1,218,194,3.426216,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-3\,B+5\,C}{2\,a^2}+\frac{2\,\left(A-B+C\right)}{a^2}\right)}{d}-\frac{\left(2\,A-5\,B+10\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,B-4\,A-\frac{40\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-3\,B+6\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A-7\,B+10\,C\right)}{a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A - 3*B + 5*C)/(2*a^2) + (2*(A - B + C))/a^2))/d - (tan(c/2 + (d*x)/2)*(2*A - 3*B + 6*C) + tan(c/2 + (d*x)/2)^5*(2*A - 5*B + 10*C) - tan(c/2 + (d*x)/2)^3*(4*A - 8*B + (40*C)/3))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 - 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 - a^2)) - (atanh(tan(c/2 + (d*x)/2))*(4*A - 7*B + 10*C))/(a^2*d) + (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
459,1,170,169,3.323645,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^2),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-2\,B+\frac{7\,C}{2}\right)}{a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B+C\right)}{2\,a^2}-\frac{2\,B-4\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-5\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-3\,C\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A - 2*B + (7*C)/2))/(a^2*d) - (tan(c/2 + (d*x)/2)*((3*(A - B + C))/(2*a^2) - (2*B - 4*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d) - (tan(c/2 + (d*x)/2)^3*(2*B - 5*C) - tan(c/2 + (d*x)/2)*(2*B - 3*C))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2))","B"
460,1,122,112,3.320259,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{a^2}-\frac{A+B-3\,C}{2\,a^2}\right)}{d}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-2\,C\right)}{a^2\,d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A - B + C)/a^2 - (A + B - 3*C)/(2*a^2)))/d + (2*atanh(tan(c/2 + (d*x)/2))*(B - 2*C))/(a^2*d) - (2*C*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) + (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
461,1,83,81,3.332320,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^2),x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{2\,a^2}-\frac{2\,A-2\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)*((A - B + C)/(2*a^2) - (2*A - 2*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
462,1,113,74,3.481123,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^2,x)","\frac{B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)-\frac{5\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}-\frac{3\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{3\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{C\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}+\frac{9\,A\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(c+d\,x\right)}{2}+\frac{3\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(c+d\,x\right)}{2}}{6\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"(B*sin((3*c)/2 + (3*d*x)/2) - (5*A*sin((3*c)/2 + (3*d*x)/2))/2 - (3*A*sin(c/2 + (d*x)/2))/2 + (3*C*sin(c/2 + (d*x)/2))/2 + (C*sin((3*c)/2 + (3*d*x)/2))/2 + (9*A*cos(c/2 + (d*x)/2)*(c + d*x))/2 + (3*A*cos((3*c)/2 + (3*d*x)/2)*(c + d*x))/2)/(6*a^2*d*cos(c/2 + (d*x)/2)^3)","B"
463,1,110,100,3.329996,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{a^2}-\frac{B-3\,A+C}{2\,a^2}\right)}{d}-\frac{x\,\left(2\,A-B\right)}{a^2}+\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A - B + C)/a^2 - (B - 3*A + C)/(2*a^2)))/d - (x*(2*A - B))/a^2 + (2*A*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
464,1,159,156,3.277014,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{x\,\left(7\,A-4\,B+2\,C\right)}{2\,a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B+C\right)}{2\,a^2}+\frac{4\,A-2\,B}{2\,a^2}\right)}{d}-\frac{\left(5\,A-2\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-2\,B\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(x*(7*A - 4*B + 2*C))/(2*a^2) - (tan(c/2 + (d*x)/2)*((3*(A - B + C))/(2*a^2) + (4*A - 2*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(5*A - 2*B) + tan(c/2 + (d*x)/2)*(3*A - 2*B))/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2)) + (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
465,1,202,185,3.343098,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\frac{\left(10\,A-5\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{40\,A}{3}-8\,B+4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A-3\,B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{x\,\left(10\,A-7\,B+4\,C\right)}{2\,a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,A-3\,B+C}{2\,a^2}+\frac{2\,\left(A-B+C\right)}{a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(6*A - 3*B + 2*C) + tan(c/2 + (d*x)/2)^5*(10*A - 5*B + 2*C) + tan(c/2 + (d*x)/2)^3*((40*A)/3 - 8*B + 4*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2)) - (x*(10*A - 7*B + 4*C))/(2*a^2) + (tan(c/2 + (d*x)/2)*((5*A - 3*B + C)/(2*a^2) + (2*(A - B + C))/a^2))/d - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
466,1,227,216,3.397821,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^3),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-3\,B+\frac{13\,C}{2}\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-3\,B+5\,C\right)}{4\,a^3}-\frac{2\,A+2\,B-10\,C}{4\,a^3}+\frac{3\,\left(A-B+C\right)}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-7\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-5\,C\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-3\,B+5\,C}{12\,a^3}+\frac{A-B+C}{4\,a^3}\right)}{d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A - 3*B + (13*C)/2))/(a^3*d) - (tan(c/2 + (d*x)/2)*((3*(A - 3*B + 5*C))/(4*a^3) - (2*A + 2*B - 10*C)/(4*a^3) + (3*(A - B + C))/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(2*B - 7*C) - tan(c/2 + (d*x)/2)*(2*B - 5*C))/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d) - (tan(c/2 + (d*x)/2)^3*((A - 3*B + 5*C)/(12*a^3) + (A - B + C)/(4*a^3)))/d","B"
467,1,176,161,3.317852,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{6\,a^3}-\frac{2\,B-4\,C}{12\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,A-6\,C}{4\,a^3}-\frac{3\,\left(A-B+C\right)}{4\,a^3}+\frac{2\,B-4\,C}{2\,a^3}\right)}{d}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-3\,C\right)}{a^3\,d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A - B + C)/(6*a^3) - (2*B - 4*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)*((2*A - 6*C)/(4*a^3) - (3*(A - B + C))/(4*a^3) + (2*B - 4*C)/(2*a^3)))/d + (2*atanh(tan(c/2 + (d*x)/2))*(B - 3*C))/(a^3*d) - (2*C*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
468,1,134,132,3.299560,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^3),x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{12\,a^3}-\frac{A+B-3\,C}{12\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-A+3\,C}{4\,a^3}+\frac{A-B+C}{4\,a^3}-\frac{A+B-3\,C}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (tan(c/2 + (d*x)/2)^3*((A - B + C)/(12*a^3) - (A + B - 3*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)*((B - A + 3*C)/(4*a^3) + (A - B + C)/(4*a^3) - (A + B - 3*C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
469,1,73,110,3.189045,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-2\,C\right)}{12\,a^3\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+C\right)}{4\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d) - (tan(c/2 + (d*x)/2)^3*(2*A - 2*C))/(12*a^3*d) + (tan(c/2 + (d*x)/2)*(A + B + C))/(4*a^3*d)","B"
470,1,158,115,3.435520,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^3,x)","\frac{A\,x}{a^3}+\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{7\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)+{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}\right)-\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(A*x)/a^3 + (cos(c/2 + (d*x)/2)^4*((B*sin(c/2 + (d*x)/2))/4 - (7*A*sin(c/2 + (d*x)/2))/4 + (C*sin(c/2 + (d*x)/2))/4) + cos(c/2 + (d*x)/2)^2*((A*sin(c/2 + (d*x)/2)^3)/3 - (B*sin(c/2 + (d*x)/2)^3)/6) - (A*sin(c/2 + (d*x)/2)^5)/20 + (B*sin(c/2 + (d*x)/2)^5)/20 - (C*sin(c/2 + (d*x)/2)^5)/20)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
471,1,164,141,3.327396,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B+C\right)}{4\,a^3}+\frac{4\,A-2\,B}{2\,a^3}+\frac{6\,A-2\,C}{4\,a^3}\right)}{d}-\frac{x\,\left(3\,A-B\right)}{a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{6\,a^3}+\frac{4\,A-2\,B}{12\,a^3}\right)}{d}+\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A - B + C))/(4*a^3) + (4*A - 2*B)/(2*a^3) + (6*A - 2*C)/(4*a^3)))/d - (x*(3*A - B))/a^3 - (tan(c/2 + (d*x)/2)^3*((A - B + C)/(6*a^3) + (4*A - 2*B)/(12*a^3)))/d + (2*A*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 + a^3)) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
472,1,215,201,3.358735,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,A-3\,B+C}{12\,a^3}+\frac{A-B+C}{4\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(5\,A-3\,B+C\right)}{4\,a^3}-\frac{2\,B-10\,A+2\,C}{4\,a^3}+\frac{3\,\left(A-B+C\right)}{2\,a^3}\right)}{d}-\frac{\left(7\,A-2\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(5\,A-2\,B\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{x\,\left(13\,A-6\,B+2\,C\right)}{2\,a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((5*A - 3*B + C)/(12*a^3) + (A - B + C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)*((3*(5*A - 3*B + C))/(4*a^3) - (2*B - 10*A + 2*C)/(4*a^3) + (3*(A - B + C))/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(7*A - 2*B) + tan(c/2 + (d*x)/2)*(5*A - 2*B))/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3)) + (x*(13*A - 6*B + 2*C))/(2*a^3) - (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
473,1,259,237,3.390912,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\frac{\left(17\,A-7\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{76\,A}{3}-12\,B+4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A-5\,B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{6\,A-4\,B+2\,C}{a^3}-\frac{5\,B-15\,A+C}{4\,a^3}+\frac{5\,\left(A-B+C\right)}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{6\,A-4\,B+2\,C}{12\,a^3}+\frac{A-B+C}{3\,a^3}\right)}{d}-\frac{x\,\left(23\,A-13\,B+6\,C\right)}{2\,a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(11*A - 5*B + 2*C) + tan(c/2 + (d*x)/2)^5*(17*A - 7*B + 2*C) + tan(c/2 + (d*x)/2)^3*((76*A)/3 - 12*B + 4*C))/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 + 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 + a^3)) + (tan(c/2 + (d*x)/2)*((6*A - 4*B + 2*C)/a^3 - (5*B - 15*A + C)/(4*a^3) + (5*(A - B + C))/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((6*A - 4*B + 2*C)/(12*a^3) + (A - B + C)/(3*a^3)))/d - (x*(23*A - 13*B + 6*C))/(2*a^3) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
474,1,296,254,3.293240,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a/cos(c + d*x))^4),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+5\,B-15\,C\right)}{8\,a^4}-\frac{3\,\left(2\,A-4\,B+6\,C\right)}{4\,a^4}-\frac{5\,\left(A-B+C\right)}{4\,a^4}+\frac{4\,A-20\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B-9\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B-7\,C\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{2\,A-4\,B+6\,C}{40\,a^4}+\frac{3\,\left(A-B+C\right)}{40\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,A-4\,B+6\,C}{8\,a^4}-\frac{A+5\,B-15\,C}{24\,a^4}+\frac{A-B+C}{4\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-4\,B+\frac{21\,C}{2}\right)}{a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A + 5*B - 15*C))/(8*a^4) - (3*(2*A - 4*B + 6*C))/(4*a^4) - (5*(A - B + C))/(4*a^4) + (4*A - 20*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*(2*B - 9*C) - tan(c/2 + (d*x)/2)*(2*B - 7*C))/(d*(a^4*tan(c/2 + (d*x)/2)^4 - 2*a^4*tan(c/2 + (d*x)/2)^2 + a^4)) - (tan(c/2 + (d*x)/2)^5*((2*A - 4*B + 6*C)/(40*a^4) + (3*(A - B + C))/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((2*A - 4*B + 6*C)/(8*a^4) - (A + 5*B - 15*C)/(24*a^4) + (A - B + C)/(4*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) + (2*atanh(tan(c/2 + (d*x)/2))*(A - 4*B + (21*C)/2))/(a^4*d)","B"
475,1,250,204,3.253087,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A-3\,B+5\,C}{40\,a^4}+\frac{A-B+C}{20\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-3\,B+5\,C}{12\,a^4}-\frac{2\,A+2\,B-10\,C}{24\,a^4}+\frac{A-B+C}{8\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-3\,B+5\,C\right)}{8\,a^4}+\frac{2\,B-2\,A+10\,C}{8\,a^4}-\frac{2\,A+2\,B-10\,C}{4\,a^4}+\frac{A-B+C}{2\,a^4}\right)}{d}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-4\,C\right)}{a^4\,d}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((A - 3*B + 5*C)/(40*a^4) + (A - B + C)/(20*a^4)))/d + (tan(c/2 + (d*x)/2)^3*((A - 3*B + 5*C)/(12*a^4) - (2*A + 2*B - 10*C)/(24*a^4) + (A - B + C)/(8*a^4)))/d + (tan(c/2 + (d*x)/2)*((3*(A - 3*B + 5*C))/(8*a^4) + (2*B - 2*A + 10*C)/(8*a^4) - (2*A + 2*B - 10*C)/(4*a^4) + (A - B + C)/(2*a^4)))/d + (2*atanh(tan(c/2 + (d*x)/2))*(B - 4*C))/(a^4*d) - (2*C*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4)) + (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d)","B"
476,1,198,173,3.250938,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,A-6\,C}{24\,a^4}-\frac{A-B+C}{24\,a^4}+\frac{2\,B-4\,C}{24\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{8\,a^4}-\frac{2\,A-6\,C}{8\,a^4}-\frac{2\,B-4\,C}{8\,a^4}+\frac{2\,B+4\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A-B+C}{40\,a^4}-\frac{2\,B-4\,C}{40\,a^4}\right)}{d}+\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((2*A - 6*C)/(24*a^4) - (A - B + C)/(24*a^4) + (2*B - 4*C)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)*((A - B + C)/(8*a^4) - (2*A - 6*C)/(8*a^4) - (2*B - 4*C)/(8*a^4) + (2*B + 4*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((A - B + C)/(40*a^4) - (2*B - 4*C)/(40*a^4)))/d + (2*C*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d)","B"
477,1,99,148,3.303629,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+B-3\,C\right)}{40\,a^4\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+C\right)}{8\,a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-A+3\,C\right)}{24\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) - (tan(c/2 + (d*x)/2)^5*(A + B - 3*C))/(40*a^4*d) + (tan(c/2 + (d*x)/2)*(A + B + C))/(8*a^4*d) + (tan(c/2 + (d*x)/2)^3*(B - A + 3*C))/(24*a^4*d)","B"
478,1,99,154,3.308544,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^4),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+C\right)}{8\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-3\,A+C\right)}{40\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A+B-C\right)}{24\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A + B + C))/(8*a^4*d) - (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) - (tan(c/2 + (d*x)/2)^5*(B - 3*A + C))/(40*a^4*d) - (tan(c/2 + (d*x)/2)^3*(3*A + B - C))/(24*a^4*d)","B"
479,1,229,148,3.690201,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^4,x)","\frac{A\,x}{a^4}+\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}-\frac{15\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}-\frac{11\,A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}-\frac{3\,B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}\right)+\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56}-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(A*x)/a^4 + (cos(c/2 + (d*x)/2)^6*((B*sin(c/2 + (d*x)/2))/8 - (15*A*sin(c/2 + (d*x)/2))/8 + (C*sin(c/2 + (d*x)/2))/8) - cos(c/2 + (d*x)/2)^4*((B*sin(c/2 + (d*x)/2)^3)/8 - (11*A*sin(c/2 + (d*x)/2)^3)/24 + (C*sin(c/2 + (d*x)/2)^3)/24) - cos(c/2 + (d*x)/2)^2*((A*sin(c/2 + (d*x)/2)^5)/8 - (3*B*sin(c/2 + (d*x)/2)^5)/40 + (C*sin(c/2 + (d*x)/2)^5)/40) + (A*sin(c/2 + (d*x)/2)^7)/56 - (B*sin(c/2 + (d*x)/2)^7)/56 + (C*sin(c/2 + (d*x)/2)^7)/56)/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
480,1,293,176,4.486222,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\frac{\frac{35\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}+\frac{167\,A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{160}+\frac{307\,A\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{480}+\frac{2263\,A\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{13440}+\frac{A\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{128}-\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}-\frac{B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}-\frac{7\,B\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{48}-\frac{13\,B\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{336}+\frac{3\,C\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{160}+\frac{C\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{160}+\frac{3\,C\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{560}-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{35\,A\,\left(c+d\,x\right)}{16}-\frac{35\,B\,\left(c+d\,x\right)}{64}\right)-\frac{21\,A\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(c+d\,x\right)}{16}-\frac{7\,A\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(c+d\,x\right)}{16}-\frac{A\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(c+d\,x\right)}{16}+\frac{21\,B\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(c+d\,x\right)}{64}+\frac{7\,B\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(c+d\,x\right)}{64}+\frac{B\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(c+d\,x\right)}{64}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"((35*A*sin(c/2 + (d*x)/2))/64 + (167*A*sin((3*c)/2 + (3*d*x)/2))/160 + (307*A*sin((5*c)/2 + (5*d*x)/2))/480 + (2263*A*sin((7*c)/2 + (7*d*x)/2))/13440 + (A*sin((9*c)/2 + (9*d*x)/2))/128 - (B*sin(c/2 + (d*x)/2))/8 - (B*sin((3*c)/2 + (3*d*x)/2))/4 - (7*B*sin((5*c)/2 + (5*d*x)/2))/48 - (13*B*sin((7*c)/2 + (7*d*x)/2))/336 + (3*C*sin((3*c)/2 + (3*d*x)/2))/160 + (C*sin((5*c)/2 + (5*d*x)/2))/160 + (3*C*sin((7*c)/2 + (7*d*x)/2))/560 - cos(c/2 + (d*x)/2)*((35*A*(c + d*x))/16 - (35*B*(c + d*x))/64) - (21*A*cos((3*c)/2 + (3*d*x)/2)*(c + d*x))/16 - (7*A*cos((5*c)/2 + (5*d*x)/2)*(c + d*x))/16 - (A*cos((7*c)/2 + (7*d*x)/2)*(c + d*x))/16 + (21*B*cos((3*c)/2 + (3*d*x)/2)*(c + d*x))/64 + (7*B*cos((5*c)/2 + (5*d*x)/2)*(c + d*x))/64 + (B*cos((7*c)/2 + (7*d*x)/2)*(c + d*x))/64)/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
481,1,285,239,3.268377,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{6\,A-4\,B+2\,C}{8\,a^4}-\frac{5\,B-15\,A+C}{24\,a^4}+\frac{A-B+C}{4\,a^4}\right)}{d}-\frac{\left(9\,A-2\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(7\,A-2\,B\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{6\,A-4\,B+2\,C}{40\,a^4}+\frac{3\,\left(A-B+C\right)}{40\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(6\,A-4\,B+2\,C\right)}{4\,a^4}-\frac{3\,\left(5\,B-15\,A+C\right)}{8\,a^4}+\frac{5\,\left(A-B+C\right)}{4\,a^4}+\frac{20\,A-4\,C}{8\,a^4}\right)}{d}+\frac{x\,\left(21\,A-8\,B+2\,C\right)}{2\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((6*A - 4*B + 2*C)/(8*a^4) - (5*B - 15*A + C)/(24*a^4) + (A - B + C)/(4*a^4)))/d - (tan(c/2 + (d*x)/2)^3*(9*A - 2*B) + tan(c/2 + (d*x)/2)*(7*A - 2*B))/(d*(2*a^4*tan(c/2 + (d*x)/2)^2 + a^4*tan(c/2 + (d*x)/2)^4 + a^4)) - (tan(c/2 + (d*x)/2)^5*((6*A - 4*B + 2*C)/(40*a^4) + (3*(A - B + C))/(40*a^4)))/d - (tan(c/2 + (d*x)/2)*((3*(6*A - 4*B + 2*C))/(4*a^4) - (3*(5*B - 15*A + C))/(8*a^4) + (5*(A - B + C))/(4*a^4) + (20*A - 4*C)/(8*a^4)))/d + (x*(21*A - 8*B + 2*C))/(2*a^4) + (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d)","B"
482,1,724,239,12.223670,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^4,x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,16{}\mathrm{i}}{11\,d}-\frac{\left(32\,A+32\,B+64\,C\right)\,1{}\mathrm{i}}{11\,d}+\frac{\left(16\,A+32\,B\right)\,1{}\mathrm{i}}{11\,d}\right)+\frac{A\,16{}\mathrm{i}}{11\,d}-\frac{\left(32\,A+32\,B+64\,C\right)\,1{}\mathrm{i}}{11\,d}+\frac{\left(16\,A+32\,B\right)\,1{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{C\,64{}\mathrm{i}}{9\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,16{}\mathrm{i}}{9\,d}+\frac{C\,256{}\mathrm{i}}{33\,d}+\frac{\left(176\,A+352\,B+704\,C\right)\,1{}\mathrm{i}}{99\,d}\right)-\frac{\left(176\,A+352\,B\right)\,1{}\mathrm{i}}{99\,d}+\frac{\left(176\,A+704\,C\right)\,1{}\mathrm{i}}{99\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,16{}\mathrm{i}}{7\,d}+\frac{\left(352\,B+896\,C\right)\,1{}\mathrm{i}}{693\,d}+\frac{\left(3168\,B+6336\,C\right)\,1{}\mathrm{i}}{693\,d}\right)+\frac{\left(1584\,A+3168\,B\right)\,1{}\mathrm{i}}{693\,d}+\frac{\left(3168\,B-6336\,C\right)\,1{}\mathrm{i}}{693\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,16{}\mathrm{i}}{5\,d}-\frac{\left(352\,B-528\,A+320\,C\right)\,1{}\mathrm{i}}{1155\,d}\right)+\frac{\left(3696\,A+7392\,B\right)\,1{}\mathrm{i}}{1155\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(3168\,A+2816\,B+2560\,C\right)\,1{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(1584\,A+1408\,B+1280\,C\right)\,1{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((exp(c*1i + d*x*1i)*((A*16i)/(5*d) - ((352*B - 528*A + 320*C)*1i)/(1155*d)) + ((3696*A + 7392*B)*1i)/(1155*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((C*64i)/(9*d) + exp(c*1i + d*x*1i)*((C*256i)/(33*d) - (A*16i)/(9*d) + ((176*A + 352*B + 704*C)*1i)/(99*d)) - ((176*A + 352*B)*1i)/(99*d) + ((176*A + 704*C)*1i)/(99*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((1584*A + 3168*B)*1i)/(693*d) - exp(c*1i + d*x*1i)*(((352*B + 896*C)*1i)/(693*d) - (A*16i)/(7*d) + ((3168*B + 6336*C)*1i)/(693*d)) + ((3168*B - 6336*C)*1i)/(693*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*16i)/(11*d) - ((32*A + 32*B + 64*C)*1i)/(11*d) + ((16*A + 32*B)*1i)/(11*d)) + (A*16i)/(11*d) - ((32*A + 32*B + 64*C)*1i)/(11*d) + ((16*A + 32*B)*1i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(3168*A + 2816*B + 2560*C)*1i)/(3465*d*(exp(c*1i + d*x*1i) + 1)) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1584*A + 1408*B + 1280*C)*1i)/(3465*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
483,1,600,193,11.426567,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(168\,A+144\,B+128\,C\right)\,1{}\mathrm{i}}{315\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,8{}\mathrm{i}}{9\,d}-\frac{\left(16\,A+16\,B+32\,C\right)\,1{}\mathrm{i}}{9\,d}+\frac{\left(8\,A+16\,B\right)\,1{}\mathrm{i}}{9\,d}\right)-\frac{A\,8{}\mathrm{i}}{9\,d}+\frac{\left(16\,A+16\,B+32\,C\right)\,1{}\mathrm{i}}{9\,d}-\frac{\left(8\,A+16\,B\right)\,1{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,8{}\mathrm{i}}{7\,d}-\frac{C\,32{}\mathrm{i}}{7\,d}-\frac{\left(72\,A+144\,B+288\,C\right)\,1{}\mathrm{i}}{63\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{C\,32{}\mathrm{i}}{63\,d}-\frac{\left(72\,A+144\,B\right)\,1{}\mathrm{i}}{63\,d}+\frac{\left(72\,A+288\,C\right)\,1{}\mathrm{i}}{63\,d}\right)\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{\left(168\,A+336\,B\right)\,1{}\mathrm{i}}{105\,d}+\frac{\left(48\,B-32\,C\right)\,1{}\mathrm{i}}{105\,d}\right)-\frac{A\,8{}\mathrm{i}}{5\,d}+\frac{\left(336\,B+672\,C\right)\,1{}\mathrm{i}}{105\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(336\,A+288\,B+256\,C\right)\,1{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*8i)/(3*d) - (exp(c*1i + d*x*1i)*(168*A + 144*B + 128*C)*1i)/(315*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*8i)/(9*d) - ((16*A + 16*B + 32*C)*1i)/(9*d) + ((8*A + 16*B)*1i)/(9*d)) - (A*8i)/(9*d) + ((16*A + 16*B + 32*C)*1i)/(9*d) - ((8*A + 16*B)*1i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*8i)/(7*d) - (C*32i)/(7*d) - ((72*A + 144*B + 288*C)*1i)/(63*d) + exp(c*1i + d*x*1i)*((C*32i)/(63*d) - ((72*A + 144*B)*1i)/(63*d) + ((72*A + 288*C)*1i)/(63*d))))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*(((168*A + 336*B)*1i)/(105*d) + ((48*B - 32*C)*1i)/(105*d)) - (A*8i)/(5*d) + ((336*B + 672*C)*1i)/(105*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(336*A + 288*B + 256*C)*1i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
484,1,479,147,7.644089,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,4{}\mathrm{i}}{3\,d}-\frac{\left(56\,B+48\,C\right)\,1{}\mathrm{i}}{105\,d}\right)+\frac{\left(140\,A+280\,B\right)\,1{}\mathrm{i}}{105\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,4{}\mathrm{i}}{7\,d}-\frac{\left(8\,A+8\,B+16\,C\right)\,1{}\mathrm{i}}{7\,d}+\frac{\left(4\,A+8\,B\right)\,1{}\mathrm{i}}{7\,d}\right)+\frac{A\,4{}\mathrm{i}}{7\,d}-\frac{\left(8\,A+8\,B+16\,C\right)\,1{}\mathrm{i}}{7\,d}+\frac{\left(4\,A+8\,B\right)\,1{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,4{}\mathrm{i}}{5\,d}+\frac{C\,16{}\mathrm{i}}{35\,d}+\frac{\left(28\,A+56\,B+112\,C\right)\,1{}\mathrm{i}}{35\,d}\right)-\frac{\left(28\,A+56\,B\right)\,1{}\mathrm{i}}{35\,d}+\frac{\left(28\,A+112\,C\right)\,1{}\mathrm{i}}{35\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(140\,A+112\,B+96\,C\right)\,1{}\mathrm{i}}{105\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*4i)/(3*d) - ((56*B + 48*C)*1i)/(105*d)) + ((140*A + 280*B)*1i)/(105*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*4i)/(7*d) - ((8*A + 8*B + 16*C)*1i)/(7*d) + ((4*A + 8*B)*1i)/(7*d)) + (A*4i)/(7*d) - ((8*A + 8*B + 16*C)*1i)/(7*d) + ((4*A + 8*B)*1i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*16i)/(35*d) - (A*4i)/(5*d) + ((28*A + 56*B + 112*C)*1i)/(35*d)) - ((28*A + 56*B)*1i)/(35*d) + ((28*A + 112*C)*1i)/(35*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(140*A + 112*B + 96*C)*1i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
485,1,246,104,6.640114,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","-\frac{2\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}-1\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(A\,15{}\mathrm{i}+B\,10{}\mathrm{i}+C\,8{}\mathrm{i}+A\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,30{}\mathrm{i}+A\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,15{}\mathrm{i}+B\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,10{}\mathrm{i}+B\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,20{}\mathrm{i}+B\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,10{}\mathrm{i}+B\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,10{}\mathrm{i}+C\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,8{}\mathrm{i}+C\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,28{}\mathrm{i}+C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}+C\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,8{}\mathrm{i}\right)}{15\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"-(2*(exp(c*1i + d*x*1i) - 1)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(A*15i + B*10i + C*8i + A*exp(c*2i + d*x*2i)*30i + A*exp(c*4i + d*x*4i)*15i + B*exp(c*1i + d*x*1i)*10i + B*exp(c*2i + d*x*2i)*20i + B*exp(c*3i + d*x*3i)*10i + B*exp(c*4i + d*x*4i)*10i + C*exp(c*1i + d*x*1i)*8i + C*exp(c*2i + d*x*2i)*28i + C*exp(c*3i + d*x*3i)*8i + C*exp(c*4i + d*x*4i)*8i))/(15*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
486,0,-1,100,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
487,0,-1,98,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
488,0,-1,117,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
489,0,-1,163,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
490,0,-1,209,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
491,1,852,243,13.526679,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{11\,d}-\frac{A\,a\,8{}\mathrm{i}}{11\,d}+\frac{a\,\left(5\,A+6\,B+4\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a\,\left(7\,A+8\,B+12\,C\right)\,8{}\mathrm{i}}{11\,d}\right)+\frac{a\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{11\,d}-\frac{A\,a\,8{}\mathrm{i}}{11\,d}+\frac{a\,\left(5\,A+6\,B+4\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a\,\left(7\,A+8\,B+12\,C\right)\,8{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(11\,B+39\,C\right)\,32{}\mathrm{i}}{693\,d}+\frac{a\,\left(A+4\,B+12\,C\right)\,8{}\mathrm{i}}{7\,d}\right)+\frac{A\,a\,8{}\mathrm{i}}{7\,d}-\frac{a\,\left(3\,A+6\,B+4\,C\right)\,8{}\mathrm{i}}{7\,d}-\frac{a\,\left(B-C\right)\,32{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{5\,d}+\frac{a\,\left(33\,A+11\,B-42\,C\right)\,16{}\mathrm{i}}{1155\,d}\right)+\frac{a\,\left(A+3\,B+2\,C\right)\,16{}\mathrm{i}}{5\,d}-\frac{A\,a\,8{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{9\,d}+\frac{a\,\left(A-8\,C\right)\,8{}\mathrm{i}}{9\,d}-\frac{C\,a\,64{}\mathrm{i}}{99\,d}-\frac{a\,\left(2\,A+3\,B+6\,C\right)\,16{}\mathrm{i}}{9\,d}\right)+\frac{A\,a\,8{}\mathrm{i}}{9\,d}+\frac{C\,a\,64{}\mathrm{i}}{9\,d}-\frac{a\,\left(2\,A+3\,B+2\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a\,\left(3\,A+2\,B+8\,C\right)\,8{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,a\,8{}\mathrm{i}}{3\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(429\,A+374\,B+336\,C\right)\,8{}\mathrm{i}}{3465\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(429\,A+374\,B+336\,C\right)\,16{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(11*B + 39*C)*32i)/(693*d) - (a*(3*A + 2*B)*8i)/(7*d) + (a*(A + 4*B + 12*C)*8i)/(7*d)) + (A*a*8i)/(7*d) - (a*(3*A + 6*B + 4*C)*8i)/(7*d) - (a*(B - C)*32i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*8i)/(11*d) - (A*a*8i)/(11*d) + (a*(5*A + 6*B + 4*C)*8i)/(11*d) - (a*(7*A + 8*B + 12*C)*8i)/(11*d)) + (a*(3*A + 2*B)*8i)/(11*d) - (A*a*8i)/(11*d) + (a*(5*A + 6*B + 4*C)*8i)/(11*d) - (a*(7*A + 8*B + 12*C)*8i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*8i)/(5*d) + (a*(33*A + 11*B - 42*C)*16i)/(1155*d)) + (a*(A + 3*B + 2*C)*16i)/(5*d) - (A*a*8i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a*8i)/(9*d) - exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*8i)/(9*d) + (a*(A - 8*C)*8i)/(9*d) - (C*a*64i)/(99*d) - (a*(2*A + 3*B + 6*C)*16i)/(9*d)) + (C*a*64i)/(9*d) - (a*(2*A + 3*B + 2*C)*16i)/(9*d) + (a*(3*A + 2*B + 8*C)*8i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a*8i)/(3*d) - (a*exp(c*1i + d*x*1i)*(429*A + 374*B + 336*C)*8i)/(3465*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(429*A + 374*B + 336*C)*16i)/(3465*d*(exp(c*1i + d*x*1i) + 1))","B"
492,1,709,187,12.338154,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,a\,4{}\mathrm{i}}{5\,d}+\frac{a\,\left(3\,A+6\,B+4\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a\,\left(3\,B+C\right)\,16{}\mathrm{i}}{105\,d}\right)-\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+4\,B+12\,C\right)\,4{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{9\,d}-\frac{A\,a\,4{}\mathrm{i}}{9\,d}+\frac{a\,\left(5\,A+6\,B+4\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a\,\left(7\,A+8\,B+12\,C\right)\,4{}\mathrm{i}}{9\,d}\right)-\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{9\,d}+\frac{A\,a\,4{}\mathrm{i}}{9\,d}-\frac{a\,\left(5\,A+6\,B+4\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a\,\left(7\,A+8\,B+12\,C\right)\,4{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a\,4{}\mathrm{i}}{3\,d}-\frac{a\,\left(21\,A+39\,B+34\,C\right)\,8{}\mathrm{i}}{315\,d}\right)+\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a\,4{}\mathrm{i}}{7\,d}+\frac{C\,a\,32{}\mathrm{i}}{63\,d}-\frac{a\,\left(2\,A+3\,B+2\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(3\,A+2\,B+8\,C\right)\,4{}\mathrm{i}}{7\,d}\right)+\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{7\,d}+\frac{a\,\left(A-8\,C\right)\,4{}\mathrm{i}}{7\,d}-\frac{a\,\left(2\,A+3\,B+6\,C\right)\,8{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(189\,A+156\,B+136\,C\right)\,4{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 6*B + 4*C)*4i)/(5*d) - (A*a*4i)/(5*d) + (a*(3*B + C)*16i)/(105*d)) - (a*(3*A + 2*B)*4i)/(5*d) + (a*(A + 4*B + 12*C)*4i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*4i)/(9*d) - (A*a*4i)/(9*d) + (a*(5*A + 6*B + 4*C)*4i)/(9*d) - (a*(7*A + 8*B + 12*C)*4i)/(9*d)) - (a*(3*A + 2*B)*4i)/(9*d) + (A*a*4i)/(9*d) - (a*(5*A + 6*B + 4*C)*4i)/(9*d) + (a*(7*A + 8*B + 12*C)*4i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a*4i)/(3*d) - (a*(21*A + 39*B + 34*C)*8i)/(315*d)) + (a*(3*A + 2*B)*4i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a*4i)/(7*d) + (C*a*32i)/(63*d) - (a*(2*A + 3*B + 2*C)*8i)/(7*d) + (a*(3*A + 2*B + 8*C)*4i)/(7*d)) + (a*(3*A + 2*B)*4i)/(7*d) + (a*(A - 8*C)*4i)/(7*d) - (a*(2*A + 3*B + 6*C)*8i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(189*A + 156*B + 136*C)*4i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
493,1,585,144,8.893595,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{A\,a\,2{}\mathrm{i}}{d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(175\,A+126\,B+104\,C\right)\,2{}\mathrm{i}}{105\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,2{}\mathrm{i}}{7\,d}-\frac{A\,a\,2{}\mathrm{i}}{7\,d}+\frac{a\,\left(5\,A+6\,B+4\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a\,\left(7\,A+8\,B+12\,C\right)\,2{}\mathrm{i}}{7\,d}\right)+\frac{a\,\left(3\,A+2\,B\right)\,2{}\mathrm{i}}{7\,d}-\frac{A\,a\,2{}\mathrm{i}}{7\,d}+\frac{a\,\left(5\,A+6\,B+4\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a\,\left(7\,A+8\,B+12\,C\right)\,2{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,2{}\mathrm{i}}{5\,d}+\frac{a\,\left(7\,A-8\,C\right)\,2{}\mathrm{i}}{35\,d}-\frac{a\,\left(2\,A+3\,B+6\,C\right)\,4{}\mathrm{i}}{5\,d}\right)-\frac{A\,a\,2{}\mathrm{i}}{5\,d}+\frac{a\,\left(2\,A+3\,B+2\,C\right)\,4{}\mathrm{i}}{5\,d}-\frac{a\,\left(3\,A+2\,B+8\,C\right)\,2{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a\,\left(3\,A+2\,B\right)\,2{}\mathrm{i}}{3\,d}-\frac{a\,\left(35\,A+28\,B+52\,C\right)\,2{}\mathrm{i}}{105\,d}\right)-\frac{A\,a\,2{}\mathrm{i}}{3\,d}+\frac{a\,\left(3\,A+6\,B+4\,C\right)\,2{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a*2i)/d - (a*exp(c*1i + d*x*1i)*(175*A + 126*B + 104*C)*2i)/(105*d)))/(exp(c*1i + d*x*1i) + 1) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*2i)/(7*d) - (A*a*2i)/(7*d) + (a*(5*A + 6*B + 4*C)*2i)/(7*d) - (a*(7*A + 8*B + 12*C)*2i)/(7*d)) + (a*(3*A + 2*B)*2i)/(7*d) - (A*a*2i)/(7*d) + (a*(5*A + 6*B + 4*C)*2i)/(7*d) - (a*(7*A + 8*B + 12*C)*2i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*2i)/(5*d) + (a*(7*A - 8*C)*2i)/(35*d) - (a*(2*A + 3*B + 6*C)*4i)/(5*d)) - (A*a*2i)/(5*d) + (a*(2*A + 3*B + 2*C)*4i)/(5*d) - (a*(3*A + 2*B + 8*C)*2i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a*(3*A + 2*B)*2i)/(3*d) - (a*(35*A + 28*B + 52*C)*2i)/(105*d)) - (A*a*2i)/(3*d) + (a*(3*A + 6*B + 4*C)*2i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
494,0,-1,142,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
495,0,-1,144,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
496,0,-1,157,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
497,0,-1,165,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
498,0,-1,215,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
499,0,-1,263,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^5*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
500,1,1201,294,17.372155,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{a^2\,\left(A-16\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{C\,a^2\,128{}\mathrm{i}}{143\,d}-\frac{a^2\,\left(3\,A+4\,B+4\,C\right)\,40{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(11\,A+10\,B+20\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{11\,d}\right)-\frac{A\,a^2\,8{}\mathrm{i}}{11\,d}-\frac{C\,a^2\,128{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(5\,A+2\,B-16\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(11\,A+10\,B+4\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(15\,A+20\,B+36\,C\right)\,8{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(A-8\,B\right)\,8{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,A+9\,B+10\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(13\,B-6\,C\right)\,64{}\mathrm{i}}{1287\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,A+5\,B+2\,C\right)\,16{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+10\,B+32\,C\right)\,8{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(B+6\,C\right)\,64{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(403\,B-572\,A+1046\,C\right)\,16{}\mathrm{i}}{15015\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{5\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(4\,A+5\,B+2\,C\right)\,16{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,8{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(6\,A+5\,B+2\,C\right)\,16{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(10\,A+11\,B+10\,C\right)\,16{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(13\,A+15\,B+20\,C\right)\,16{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{13\,d}\right)-\frac{A\,a^2\,8{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(6\,A+5\,B+2\,C\right)\,16{}\mathrm{i}}{13\,d}+\frac{a^2\,\left(10\,A+11\,B+10\,C\right)\,16{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(13\,A+15\,B+20\,C\right)\,16{}\mathrm{i}}{13\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{13\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^6}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(5\,A+16\,B+20\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(143\,A+650\,B+811\,C\right)\,32{}\mathrm{i}}{9009\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{7\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(A-7\,C\right)\,32{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(9\,A+10\,B+4\,C\right)\,8{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left(\frac{A\,a^2\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(10439\,A+9230\,B+8368\,C\right)\,8{}\mathrm{i}}{45045\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(10439\,A+9230\,B+8368\,C\right)\,16{}\mathrm{i}}{45045\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*8i)/(13*d) - (a^2*(6*A + 5*B + 2*C)*16i)/(13*d) - (a^2*(10*A + 11*B + 10*C)*16i)/(13*d) + (a^2*(13*A + 15*B + 20*C)*16i)/(13*d) + (a^2*(5*A + 2*B)*8i)/(13*d)) - (A*a^2*8i)/(13*d) + (a^2*(6*A + 5*B + 2*C)*16i)/(13*d) + (a^2*(10*A + 11*B + 10*C)*16i)/(13*d) - (a^2*(13*A + 15*B + 20*C)*16i)/(13*d) - (a^2*(5*A + 2*B)*8i)/(13*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^6) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((A*a^2*8i)/(9*d) - exp(c*1i + d*x*1i)*((a^2*(A - 8*B)*8i)/(9*d) - (a^2*(5*A + 9*B + 10*C)*16i)/(9*d) + (a^2*(5*A + 2*B)*8i)/(9*d) - (a^2*(13*B - 6*C)*64i)/(1287*d)) - (a^2*(5*A + 5*B + 2*C)*16i)/(9*d) + (a^2*(5*A + 10*B + 32*C)*8i)/(9*d) + (a^2*(B + 6*C)*64i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(403*B - 572*A + 1046*C)*16i)/(15015*d) - (a^2*(5*A + 2*B)*8i)/(5*d)) + (A*a^2*8i)/(5*d) - (a^2*(4*A + 5*B + 2*C)*16i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((C*a^2*128i)/(143*d) - (a^2*(A - 16*C)*8i)/(11*d) - (a^2*(3*A + 4*B + 4*C)*40i)/(11*d) + (a^2*(11*A + 10*B + 20*C)*8i)/(11*d) + (a^2*(5*A + 2*B)*8i)/(11*d)) - (A*a^2*8i)/(11*d) - (C*a^2*128i)/(11*d) + (a^2*(5*A + 2*B - 16*C)*8i)/(11*d) + (a^2*(11*A + 10*B + 4*C)*8i)/(11*d) - (a^2*(15*A + 20*B + 36*C)*8i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(5*A + 16*B + 20*C)*8i)/(7*d) + (a^2*(143*A + 650*B + 811*C)*32i)/(9009*d) - (a^2*(5*A + 2*B)*8i)/(7*d)) + (A*a^2*8i)/(7*d) - (a^2*(A - 7*C)*32i)/(7*d) - (a^2*(9*A + 10*B + 4*C)*8i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + (((A*a^2*8i)/(3*d) - (a^2*exp(c*1i + d*x*1i)*(10439*A + 9230*B + 8368*C)*8i)/(45045*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(10439*A + 9230*B + 8368*C)*16i)/(45045*d*(exp(c*1i + d*x*1i) + 1))","B"
501,1,1034,229,17.049392,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(-\frac{A\,a^2\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(9\,A+10\,B+4\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(33\,A+44\,B-31\,C\right)\,16{}\mathrm{i}}{1155\,d}\right)+\frac{a^2\,\left(5\,A+16\,B+20\,C\right)\,4{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(6\,A+5\,B+2\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(10\,A+11\,B+10\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(13\,A+15\,B+20\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{11\,d}\right)+\frac{A\,a^2\,4{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(6\,A+5\,B+2\,C\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(10\,A+11\,B+10\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(13\,A+15\,B+20\,C\right)\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{9\,d}+\frac{C\,a^2\,64{}\mathrm{i}}{99\,d}-\frac{a^2\,\left(5\,A+2\,B-16\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(11\,A+10\,B+4\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(15\,A+20\,B+36\,C\right)\,4{}\mathrm{i}}{9\,d}\right)-\frac{a^2\,\left(A-16\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(3\,A+4\,B+4\,C\right)\,20{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(11\,A+10\,B+20\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+5\,B+2\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,A+10\,B+32\,C\right)\,4{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(11\,B+50\,C\right)\,32{}\mathrm{i}}{693\,d}\right)+\frac{a^2\,\left(A-8\,B\right)\,4{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+9\,B+10\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,4{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(660\,A+803\,B+710\,C\right)\,8{}\mathrm{i}}{3465\,d}\right)+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(3795\,A+3212\,B+2840\,C\right)\,4{}\mathrm{i}}{3465\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(9*A + 10*B + 4*C)*4i)/(5*d) - (A*a^2*4i)/(5*d) + (a^2*(33*A + 44*B - 31*C)*16i)/(1155*d)) + (a^2*(5*A + 16*B + 20*C)*4i)/(5*d) - (a^2*(5*A + 2*B)*4i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(11*d) - (a^2*(6*A + 5*B + 2*C)*8i)/(11*d) - (a^2*(10*A + 11*B + 10*C)*8i)/(11*d) + (a^2*(13*A + 15*B + 20*C)*8i)/(11*d) + (a^2*(5*A + 2*B)*4i)/(11*d)) + (A*a^2*4i)/(11*d) - (a^2*(6*A + 5*B + 2*C)*8i)/(11*d) - (a^2*(10*A + 11*B + 10*C)*8i)/(11*d) + (a^2*(13*A + 15*B + 20*C)*8i)/(11*d) + (a^2*(5*A + 2*B)*4i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(9*d) + (C*a^2*64i)/(99*d) - (a^2*(5*A + 2*B - 16*C)*4i)/(9*d) - (a^2*(11*A + 10*B + 4*C)*4i)/(9*d) + (a^2*(15*A + 20*B + 36*C)*4i)/(9*d)) - (a^2*(A - 16*C)*4i)/(9*d) - (a^2*(3*A + 4*B + 4*C)*20i)/(9*d) + (a^2*(11*A + 10*B + 20*C)*4i)/(9*d) + (a^2*(5*A + 2*B)*4i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(7*d) - (a^2*(5*A + 5*B + 2*C)*8i)/(7*d) + (a^2*(5*A + 10*B + 32*C)*4i)/(7*d) + (a^2*(11*B + 50*C)*32i)/(693*d)) + (a^2*(A - 8*B)*4i)/(7*d) - (a^2*(5*A + 9*B + 10*C)*8i)/(7*d) + (a^2*(5*A + 2*B)*4i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*4i)/(3*d) - (a^2*(660*A + 803*B + 710*C)*8i)/(3465*d)) + (a^2*(5*A + 2*B)*4i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(3795*A + 3212*B + 2840*C)*4i)/(3465*d*(exp(c*1i + d*x*1i) + 1))","B"
502,1,885,184,16.795081,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\left(\frac{A\,a^2\,2{}\mathrm{i}}{d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(903\,A+690\,B+584\,C\right)\,2{}\mathrm{i}}{315\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(3\,A+4\,B+4\,C\right)\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(11\,A+10\,B+20\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(9\,A-16\,C\right)\,2{}\mathrm{i}}{63\,d}\right)+\frac{A\,a^2\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+2\,B-16\,C\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(11\,A+10\,B+4\,C\right)\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(15\,A+20\,B+36\,C\right)\,2{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(189\,A+240\,B+292\,C\right)\,2{}\mathrm{i}}{315\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{3\,d}\right)+\frac{A\,a^2\,2{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(9\,A+10\,B+4\,C\right)\,2{}\mathrm{i}}{3\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{A\,a^2\,2{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(6\,A+5\,B+2\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(10\,A+11\,B+10\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(13\,A+15\,B+20\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{9\,d}\right)-\frac{A\,a^2\,2{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(6\,A+5\,B+2\,C\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(10\,A+11\,B+10\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(13\,A+15\,B+20\,C\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{a^2\,\left(5\,A+9\,B+10\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(24\,B-21\,A+32\,C\right)\,2{}\mathrm{i}}{105\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{5\,d}\right)+\frac{A\,a^2\,2{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(5\,A+5\,B+2\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(5\,A+10\,B+32\,C\right)\,2{}\mathrm{i}}{5\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"(((A*a^2*2i)/d - (a^2*exp(c*1i + d*x*1i)*(903*A + 690*B + 584*C)*2i)/(315*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/(exp(c*1i + d*x*1i) + 1) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(3*A + 4*B + 4*C)*10i)/(7*d) - (a^2*(11*A + 10*B + 20*C)*2i)/(7*d) - (a^2*(5*A + 2*B)*2i)/(7*d) + (a^2*(9*A - 16*C)*2i)/(63*d)) + (A*a^2*2i)/(7*d) - (a^2*(5*A + 2*B - 16*C)*2i)/(7*d) - (a^2*(11*A + 10*B + 4*C)*2i)/(7*d) + (a^2*(15*A + 20*B + 36*C)*2i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(189*A + 240*B + 292*C)*2i)/(315*d) - (a^2*(5*A + 2*B)*2i)/(3*d)) + (A*a^2*2i)/(3*d) - (a^2*(9*A + 10*B + 4*C)*2i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((A*a^2*2i)/(9*d) - (a^2*(6*A + 5*B + 2*C)*4i)/(9*d) - (a^2*(10*A + 11*B + 10*C)*4i)/(9*d) + (a^2*(13*A + 15*B + 20*C)*4i)/(9*d) + (a^2*(5*A + 2*B)*2i)/(9*d)) - (A*a^2*2i)/(9*d) + (a^2*(6*A + 5*B + 2*C)*4i)/(9*d) + (a^2*(10*A + 11*B + 10*C)*4i)/(9*d) - (a^2*(13*A + 15*B + 20*C)*4i)/(9*d) - (a^2*(5*A + 2*B)*2i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*((a^2*(5*A + 9*B + 10*C)*4i)/(5*d) + (a^2*(24*B - 21*A + 32*C)*2i)/(105*d) - (a^2*(5*A + 2*B)*2i)/(5*d)) + (A*a^2*2i)/(5*d) - (a^2*(5*A + 5*B + 2*C)*4i)/(5*d) + (a^2*(5*A + 10*B + 32*C)*2i)/(5*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
503,0,-1,182,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
504,0,-1,184,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
505,0,-1,197,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
506,0,-1,207,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
507,0,-1,215,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
508,0,-1,261,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^5*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
509,0,-1,311,0.000000,"\text{Not used}","int(cos(c + d*x)^6*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^6\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^6*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
510,0,-1,254,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)), x)","F"
511,0,-1,208,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)), x)","F"
512,0,-1,164,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)), x)","F"
513,0,-1,118,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)), x)","F"
514,0,-1,118,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/2), x)","F"
515,0,-1,120,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
516,0,-1,169,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
517,0,-1,213,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
518,0,-1,259,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
519,0,-1,277,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)), x)","F"
520,0,-1,229,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)), x)","F"
521,0,-1,181,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)), x)","F"
522,0,-1,120,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)), x)","F"
523,0,-1,131,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(3/2), x)","F"
524,0,-1,173,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
525,0,-1,232,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
526,0,-1,284,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
527,0,-1,277,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)), x)","F"
528,0,-1,227,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)), x)","F"
529,0,-1,179,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)), x)","F"
530,0,-1,137,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)), x)","F"
531,0,-1,171,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/2), x)","F"
532,0,-1,217,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
533,0,-1,280,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
534,0,-1,217,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
535,0,-1,181,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
536,0,-1,143,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
537,0,-1,138,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
538,0,-1,146,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
539,0,-1,182,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
540,0,-1,215,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
541,0,-1,291,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
542,0,-1,255,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
543,0,-1,214,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
544,0,-1,208,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
545,0,-1,214,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
546,0,-1,219,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
547,0,-1,255,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
548,0,-1,291,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2), x)","F"
549,0,-1,343,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
550,0,-1,307,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
551,0,-1,271,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
552,0,-1,271,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
553,0,-1,270,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
554,0,-1,271,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
555,0,-1,271,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
556,0,-1,307,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2), x)","F"
557,0,-1,343,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(13/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(13/2), x)","F"
558,0,-1,250,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
559,0,-1,205,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
560,0,-1,162,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
561,0,-1,133,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
562,0,-1,174,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
563,0,-1,214,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)), x)","F"
564,0,-1,250,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(7/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(7/2)), x)","F"
565,0,-1,251,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
566,0,-1,207,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
567,0,-1,173,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
568,0,-1,184,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
569,0,-1,220,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
570,0,-1,254,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)), x)","F"
571,0,-1,308,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
572,0,-1,269,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
573,0,-1,231,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
574,0,-1,231,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
575,0,-1,241,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
576,0,-1,274,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
577,0,-1,313,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)), x)","F"
578,0,-1,227,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
579,0,-1,179,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
580,0,-1,131,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
581,0,-1,119,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
582,0,-1,120,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
583,1,115,129,4.985625,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(35\,A\,\sin\left(c+d\,x\right)+40\,B\,\sin\left(c+d\,x\right)+60\,C\,\sin\left(c+d\,x\right)+8\,A\,\sin\left(2\,c+2\,d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)\right)}{30\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(35*A*sin(c + d*x) + 40*B*sin(c + d*x) + 60*C*sin(c + d*x) + 8*A*sin(2*c + 2*d*x) + 3*A*sin(3*c + 3*d*x) + 10*B*sin(2*c + 2*d*x)))/(30*d*(cos(c + d*x) + 1))","B"
584,1,151,178,6.198456,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(420\,A\,\sin\left(c+d\,x\right)+490\,B\,\sin\left(c+d\,x\right)+560\,C\,\sin\left(c+d\,x\right)+126\,A\,\sin\left(2\,c+2\,d\,x\right)+36\,A\,\sin\left(3\,c+3\,d\,x\right)+15\,A\,\sin\left(4\,c+4\,d\,x\right)+112\,B\,\sin\left(2\,c+2\,d\,x\right)+42\,B\,\sin\left(3\,c+3\,d\,x\right)+140\,C\,\sin\left(2\,c+2\,d\,x\right)\right)}{420\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(420*A*sin(c + d*x) + 490*B*sin(c + d*x) + 560*C*sin(c + d*x) + 126*A*sin(2*c + 2*d*x) + 36*A*sin(3*c + 3*d*x) + 15*A*sin(4*c + 4*d*x) + 112*B*sin(2*c + 2*d*x) + 42*B*sin(3*c + 3*d*x) + 140*C*sin(2*c + 2*d*x)))/(420*d*(cos(c + d*x) + 1))","B"
585,1,187,226,7.765277,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(2310\,A\,\sin\left(c+d\,x\right)+2520\,B\,\sin\left(c+d\,x\right)+2940\,C\,\sin\left(c+d\,x\right)+672\,A\,\sin\left(2\,c+2\,d\,x\right)+297\,A\,\sin\left(3\,c+3\,d\,x\right)+80\,A\,\sin\left(4\,c+4\,d\,x\right)+35\,A\,\sin\left(5\,c+5\,d\,x\right)+756\,B\,\sin\left(2\,c+2\,d\,x\right)+216\,B\,\sin\left(3\,c+3\,d\,x\right)+90\,B\,\sin\left(4\,c+4\,d\,x\right)+672\,C\,\sin\left(2\,c+2\,d\,x\right)+252\,C\,\sin\left(3\,c+3\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(2310*A*sin(c + d*x) + 2520*B*sin(c + d*x) + 2940*C*sin(c + d*x) + 672*A*sin(2*c + 2*d*x) + 297*A*sin(3*c + 3*d*x) + 80*A*sin(4*c + 4*d*x) + 35*A*sin(5*c + 5*d*x) + 756*B*sin(2*c + 2*d*x) + 216*B*sin(3*c + 3*d*x) + 90*B*sin(4*c + 4*d*x) + 672*C*sin(2*c + 2*d*x) + 252*C*sin(3*c + 3*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
586,0,-1,283,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
587,0,-1,233,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
588,0,-1,181,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
589,0,-1,183,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
590,0,-1,177,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
591,0,-1,172,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
592,1,152,181,6.354125,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(910\,A\,\sin\left(c+d\,x\right)+1050\,B\,\sin\left(c+d\,x\right)+1400\,C\,\sin\left(c+d\,x\right)+238\,A\,\sin\left(2\,c+2\,d\,x\right)+78\,A\,\sin\left(3\,c+3\,d\,x\right)+15\,A\,\sin\left(4\,c+4\,d\,x\right)+252\,B\,\sin\left(2\,c+2\,d\,x\right)+42\,B\,\sin\left(3\,c+3\,d\,x\right)+140\,C\,\sin\left(2\,c+2\,d\,x\right)\right)}{420\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(910*A*sin(c + d*x) + 1050*B*sin(c + d*x) + 1400*C*sin(c + d*x) + 238*A*sin(2*c + 2*d*x) + 78*A*sin(3*c + 3*d*x) + 15*A*sin(4*c + 4*d*x) + 252*B*sin(2*c + 2*d*x) + 42*B*sin(3*c + 3*d*x) + 140*C*sin(2*c + 2*d*x)))/(420*d*(cos(c + d*x) + 1))","B"
593,1,188,232,8.031708,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(4830\,A\,\sin\left(c+d\,x\right)+5460\,B\,\sin\left(c+d\,x\right)+6300\,C\,\sin\left(c+d\,x\right)+1428\,A\,\sin\left(2\,c+2\,d\,x\right)+513\,A\,\sin\left(3\,c+3\,d\,x\right)+170\,A\,\sin\left(4\,c+4\,d\,x\right)+35\,A\,\sin\left(5\,c+5\,d\,x\right)+1428\,B\,\sin\left(2\,c+2\,d\,x\right)+468\,B\,\sin\left(3\,c+3\,d\,x\right)+90\,B\,\sin\left(4\,c+4\,d\,x\right)+1512\,C\,\sin\left(2\,c+2\,d\,x\right)+252\,C\,\sin\left(3\,c+3\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(4830*A*sin(c + d*x) + 5460*B*sin(c + d*x) + 6300*C*sin(c + d*x) + 1428*A*sin(2*c + 2*d*x) + 513*A*sin(3*c + 3*d*x) + 170*A*sin(4*c + 4*d*x) + 35*A*sin(5*c + 5*d*x) + 1428*B*sin(2*c + 2*d*x) + 468*B*sin(3*c + 3*d*x) + 90*B*sin(4*c + 4*d*x) + 1512*C*sin(2*c + 2*d*x) + 252*C*sin(3*c + 3*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
594,1,392,284,11.485245,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{a\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(3\,A+2\,B\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{72\,d}+\frac{A\,a\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{88\,d}+\frac{a\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(7\,A+6\,B+4\,C\right)}{56\,d}+\frac{a\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(9\,A+10\,B+10\,C\right)}{12\,d}+\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(11\,A+12\,B+14\,C\right)}{4\,d}+\frac{a\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(13\,A+12\,B+12\,C\right)}{40\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((11*c)/2 + (11*d*x)/2)*1i + 2*sin((11*c)/4 + (11*d*x)/4)^2 - 1)*((a*sin((9*c)/2 + (9*d*x)/2)*(3*A + 2*B)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(72*d) + (A*a*sin((11*c)/2 + (11*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(88*d) + (a*sin((7*c)/2 + (7*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(7*A + 6*B + 4*C))/(56*d) + (a*sin((3*c)/2 + (3*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(9*A + 10*B + 10*C))/(12*d) + (a*sin(c/2 + (d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(11*A + 12*B + 14*C))/(4*d) + (a*sin((5*c)/2 + (5*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(13*A + 12*B + 12*C))/(40*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
595,0,-1,333,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
596,0,-1,281,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
597,0,-1,233,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
598,0,-1,233,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
599,0,-1,233,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
600,0,-1,223,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
601,0,-1,222,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
602,1,190,231,8.020567,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\frac{a^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(10290\,A\,\sin\left(c+d\,x\right)+11760\,B\,\sin\left(c+d\,x\right)+14700\,C\,\sin\left(c+d\,x\right)+2856\,A\,\sin\left(2\,c+2\,d\,x\right)+981\,A\,\sin\left(3\,c+3\,d\,x\right)+260\,A\,\sin\left(4\,c+4\,d\,x\right)+35\,A\,\sin\left(5\,c+5\,d\,x\right)+2940\,B\,\sin\left(2\,c+2\,d\,x\right)+720\,B\,\sin\left(3\,c+3\,d\,x\right)+90\,B\,\sin\left(4\,c+4\,d\,x\right)+2352\,C\,\sin\left(2\,c+2\,d\,x\right)+252\,C\,\sin\left(3\,c+3\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a^2*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(10290*A*sin(c + d*x) + 11760*B*sin(c + d*x) + 14700*C*sin(c + d*x) + 2856*A*sin(2*c + 2*d*x) + 981*A*sin(3*c + 3*d*x) + 260*A*sin(4*c + 4*d*x) + 35*A*sin(5*c + 5*d*x) + 2940*B*sin(2*c + 2*d*x) + 720*B*sin(3*c + 3*d*x) + 90*B*sin(4*c + 4*d*x) + 2352*C*sin(2*c + 2*d*x) + 252*C*sin(3*c + 3*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
603,1,404,284,11.313072,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{A\,a^2\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{88\,d}+\frac{a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(13\,A+10\,B+4\,C\right)}{56\,d}+\frac{a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(19\,A+20\,B+22\,C\right)}{12\,d}+\frac{a^2\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(25\,A+24\,B+20\,C\right)}{40\,d}+\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(23\,A+26\,B+30\,C\right)}{4\,d}+\frac{a^2\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(5\,A+2\,B\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{72\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((11*c)/2 + (11*d*x)/2)*1i + 2*sin((11*c)/4 + (11*d*x)/4)^2 - 1)*((A*a^2*sin((11*c)/2 + (11*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(88*d) + (a^2*sin((7*c)/2 + (7*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(13*A + 10*B + 4*C))/(56*d) + (a^2*sin((3*c)/2 + (3*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(19*A + 20*B + 22*C))/(12*d) + (a^2*sin((5*c)/2 + (5*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(25*A + 24*B + 20*C))/(40*d) + (a^2*sin(c/2 + (d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1)*(23*A + 26*B + 30*C))/(4*d) + (a^2*sin((9*c)/2 + (9*d*x)/2)*(5*A + 2*B)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(72*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
604,1,458,334,12.738480,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(13/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{A\,a^2\,\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{208\,d}+\frac{a^2\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(7\,A+5\,B+2\,C\right)}{72\,d}+\frac{a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(15\,A+13\,B+10\,C\right)}{56\,d}+\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(21\,A+23\,B+26\,C\right)}{4\,d}+\frac{a^2\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(51\,A+50\,B+48\,C\right)}{80\,d}+\frac{a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)\,\left(71\,A+76\,B+80\,C\right)}{48\,d}+\frac{a^2\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(5\,A+2\,B\right)\,\left(-2\,{\sin\left(\frac{13\,c}{4}+\frac{13\,d\,x}{4}\right)}^2+\sin\left(\frac{13\,c}{2}+\frac{13\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{176\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((13*c)/2 + (13*d*x)/2)*1i + 2*sin((13*c)/4 + (13*d*x)/4)^2 - 1)*((A*a^2*sin((13*c)/2 + (13*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(208*d) + (a^2*sin((9*c)/2 + (9*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1)*(7*A + 5*B + 2*C))/(72*d) + (a^2*sin((7*c)/2 + (7*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1)*(15*A + 13*B + 10*C))/(56*d) + (a^2*sin(c/2 + (d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1)*(21*A + 23*B + 26*C))/(4*d) + (a^2*sin((5*c)/2 + (5*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1)*(51*A + 50*B + 48*C))/(80*d) + (a^2*sin((3*c)/2 + (3*d*x)/2)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1)*(71*A + 76*B + 80*C))/(48*d) + (a^2*sin((11*c)/2 + (11*d*x)/2)*(5*A + 2*B)*(sin((13*c)/2 + (13*d*x)/2)*1i - 2*sin((13*c)/4 + (13*d*x)/4)^2 + 1))/(176*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
605,0,-1,241,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
606,0,-1,195,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
607,0,-1,141,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
608,0,-1,138,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
609,0,-1,143,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
610,0,-1,191,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
611,0,-1,237,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)), x)","F"
612,0,-1,152,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A\,a+\frac{A\,b+B\,a}{\cos\left(c+d\,x\right)}+\frac{B\,b}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
613,0,-1,260,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
614,0,-1,202,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
615,0,-1,149,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
616,0,-1,161,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
617,0,-1,213,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
618,0,-1,263,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
619,0,-1,254,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
620,0,-1,201,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
621,0,-1,163,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
622,0,-1,211,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
623,0,-1,261,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
624,0,-1,313,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)), x)","F"
625,0,-1,446,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
626,0,-1,390,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(1/3), x)","F"
627,0,-1,402,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(4/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(4/3), x)","F"
628,0,-1,466,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(7/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(7/3), x)","F"
629,0,-1,839,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{4/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(4/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
630,0,-1,786,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
631,0,-1,803,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(2/3), x)","F"
632,0,-1,856,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + a/cos(c + d*x))^(5/3), x)","F"
633,0,-1,259,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^n*(1/cos(c + d*x))^m*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
634,0,-1,258,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(n + 1),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{n+1}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(n + 1), x)","F"
635,0,-1,38,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(n + 1) - ((a + a/cos(c + d*x))^n*(a*(B + A*n + B*n) + (C*a*(n + 1))/cos(c + d*x)))/(a*(1/cos(c + d*x))^n*(n + 1)),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{n+1}}-\frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,\left(a\,\left(B+A\,n+B\,n\right)+\frac{C\,a\,\left(n+1\right)}{\cos\left(c+d\,x\right)}\right)}{a\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^n\,\left(n+1\right)} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^n*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(n + 1) - ((a + a/cos(c + d*x))^n*(a*(B + A*n + B*n) + (C*a*(n + 1))/cos(c + d*x)))/(a*(1/cos(c + d*x))^n*(n + 1)), x)","F"
636,0,-1,171,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^m*(B - C + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^m\,\left(B-C+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + a/cos(c + d*x))^m*(B - C + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
637,1,232,140,7.679526,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+3\,C\right)}{4\,d}-\frac{\left(2\,A\,b-A\,a-\frac{5\,C\,a}{4}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,a-\frac{16\,A\,b}{3}+\frac{C\,a}{2}-\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b}{3}+\frac{116\,C\,b}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-2\,A\,a-\frac{16\,A\,b}{3}-\frac{C\,a}{2}-\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a+2\,A\,b+\frac{5\,C\,a}{4}+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(4*A + 3*C))/(4*d) - (tan(c/2 + (d*x)/2)*(A*a + 2*A*b + (5*C*a)/4 + 2*C*b) + tan(c/2 + (d*x)/2)^5*((20*A*b)/3 + (116*C*b)/15) - tan(c/2 + (d*x)/2)^9*(A*a - 2*A*b + (5*C*a)/4 - 2*C*b) - tan(c/2 + (d*x)/2)^3*(2*A*a + (16*A*b)/3 + (C*a)/2 + (8*C*b)/3) + tan(c/2 + (d*x)/2)^7*(2*A*a - (16*A*b)/3 + (C*a)/2 - (8*C*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
638,1,197,117,7.640536,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(A\,b-2\,A\,a-2\,C\,a+\frac{5\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a-A\,b+\frac{10\,C\,a}{3}+\frac{3\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,C\,b}{4}-A\,b-\frac{10\,C\,a}{3}-6\,A\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+A\,b+2\,C\,a+\frac{5\,C\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a + A*b + 2*C*a + (5*C*b)/4) - tan(c/2 + (d*x)/2)^7*(2*A*a - A*b + 2*C*a - (5*C*b)/4) - tan(c/2 + (d*x)/2)^3*(6*A*a + A*b + (10*C*a)/3 - (3*C*b)/4) + tan(c/2 + (d*x)/2)^5*(6*A*a - A*b + (10*C*a)/3 + (3*C*b)/4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (b*atanh(tan(c/2 + (d*x)/2))*(4*A + 3*C))/(4*d)","B"
639,1,137,86,5.829090,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)))/cos(c + d*x),x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,A+C\right)}{d}-\frac{\left(2\,A\,b-C\,a+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,b-\frac{4\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(2*A + C))/d - (tan(c/2 + (d*x)/2)*(2*A*b + C*a + 2*C*b) - tan(c/2 + (d*x)/2)^3*(4*A*b + (4*C*b)/3) + tan(c/2 + (d*x)/2)^5*(2*A*b - C*a + 2*C*b))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
640,1,135,58,3.627442,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,b\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{A\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}","Not used",1,"(2*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (A*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d + (C*a*sin(c + d*x))/(d*cos(c + d*x)) + (C*b*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
641,1,91,42,3.508296,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(A*a*sin(c + d*x))/d + (2*A*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b*sin(c + d*x))/(d*cos(c + d*x))","B"
642,1,115,58,3.670435,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{A\,b\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*b*sin(c + d*x))/d + (A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(2*c + 2*d*x))/(4*d)","B"
643,1,67,77,3.531686,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{A\,b\,x}{2}+C\,b\,x+\frac{3\,A\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{A\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*b*x)/2 + C*b*x + (3*A*a*sin(c + d*x))/(4*d) + (C*a*sin(c + d*x))/d + (A*a*sin(3*c + 3*d*x))/(12*d) + (A*b*sin(2*c + 2*d*x))/(4*d)","B"
644,1,215,95,6.473507,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{\left(2\,A\,b-\frac{5\,A\,a}{4}-C\,a+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a}{4}+\frac{10\,A\,b}{3}-C\,a+6\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{10\,A\,b}{3}-\frac{3\,A\,a}{4}+C\,a+6\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a}{4}+2\,A\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,C\right)}{4\,\left(\frac{3\,A\,a}{4}+C\,a\right)}\right)\,\left(3\,A+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*a)/4 + 2*A*b + C*a + 2*C*b) - tan(c/2 + (d*x)/2)^7*((5*A*a)/4 - 2*A*b + C*a - 2*C*b) + tan(c/2 + (d*x)/2)^3*((10*A*b)/3 - (3*A*a)/4 + C*a + 6*C*b) + tan(c/2 + (d*x)/2)^5*((3*A*a)/4 + (10*A*b)/3 - C*a + 6*C*b))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(3*A + 4*C))/(4*((3*A*a)/4 + C*a)))*(3*A + 4*C))/(4*d)","B"
645,1,250,131,6.495954,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{\left(2\,A\,a-\frac{5\,A\,b}{4}+2\,C\,a-C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a}{3}-\frac{A\,b}{2}+\frac{16\,C\,a}{3}-2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a}{3}+\frac{A\,b}{2}+\frac{16\,C\,a}{3}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+\frac{5\,A\,b}{4}+2\,C\,a+C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,C\right)}{4\,\left(\frac{3\,A\,b}{4}+C\,b\right)}\right)\,\left(3\,A+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a + (5*A*b)/4 + 2*C*a + C*b) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*C*a)/3) + tan(c/2 + (d*x)/2)^9*(2*A*a - (5*A*b)/4 + 2*C*a - C*b) + tan(c/2 + (d*x)/2)^3*((8*A*a)/3 + (A*b)/2 + (16*C*a)/3 + 2*C*b) + tan(c/2 + (d*x)/2)^7*((8*A*a)/3 - (A*b)/2 + (16*C*a)/3 - 2*C*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (b*atan((b*tan(c/2 + (d*x)/2)*(3*A + 4*C))/(4*((3*A*b)/4 + C*b)))*(3*A + 4*C))/(4*d)","B"
646,1,322,226,7.551111,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+3\,C\right)}{2\,d}-\frac{\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2-2\,A\,a\,b-\frac{5\,C\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(4\,A\,a\,b-\frac{16\,A\,b^2}{3}-\frac{16\,C\,a^2}{3}-\frac{8\,C\,b^2}{3}-8\,A\,a^2+C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,A\,a^2+\frac{20\,A\,b^2}{3}+\frac{20\,C\,a^2}{3}+\frac{116\,C\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,A\,a^2-\frac{16\,A\,b^2}{3}-\frac{16\,C\,a^2}{3}-\frac{8\,C\,b^2}{3}-4\,A\,a\,b-C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2+2\,A\,a\,b+\frac{5\,C\,a\,b}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*b*atanh(tan(c/2 + (d*x)/2))*(4*A + 3*C))/(2*d) - (tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 - 2*A*a*b - (5*C*a*b)/2) - tan(c/2 + (d*x)/2)^3*(8*A*a^2 + (16*A*b^2)/3 + (16*C*a^2)/3 + (8*C*b^2)/3 + 4*A*a*b + C*a*b) - tan(c/2 + (d*x)/2)^7*(8*A*a^2 + (16*A*b^2)/3 + (16*C*a^2)/3 + (8*C*b^2)/3 - 4*A*a*b - C*a*b) + tan(c/2 + (d*x)/2)^5*(12*A*a^2 + (20*A*b^2)/3 + (20*C*a^2)/3 + (116*C*b^2)/15) + tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 + 2*A*a*b + (5*C*a*b)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
647,1,307,170,7.374648,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2)/cos(c + d*x),x)","\frac{\left(A\,b^2+C\,a^2+\frac{5\,C\,b^2}{4}-4\,A\,a\,b-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,C\,b^2}{4}-C\,a^2-A\,b^2+12\,A\,a\,b+\frac{20\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,C\,b^2}{4}-C\,a^2-A\,b^2-12\,A\,a\,b-\frac{20\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,b^2+C\,a^2+\frac{5\,C\,b^2}{4}+4\,A\,a\,b+4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2+\frac{A\,b^2}{2}+\frac{C\,a^2}{2}+\frac{3\,C\,b^2}{8}\right)}{4\,A\,a^2+2\,A\,b^2+2\,C\,a^2+\frac{3\,C\,b^2}{2}}\right)\,\left(2\,A\,a^2+A\,b^2+C\,a^2+\frac{3\,C\,b^2}{4}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 + (5*C*b^2)/4 + 4*A*a*b + 4*C*a*b) + tan(c/2 + (d*x)/2)^7*(A*b^2 + C*a^2 + (5*C*b^2)/4 - 4*A*a*b - 4*C*a*b) - tan(c/2 + (d*x)/2)^3*(A*b^2 + C*a^2 - (3*C*b^2)/4 + 12*A*a*b + (20*C*a*b)/3) + tan(c/2 + (d*x)/2)^5*((3*C*b^2)/4 - C*a^2 - A*b^2 + 12*A*a*b + (20*C*a*b)/3))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*(A*a^2 + (A*b^2)/2 + (C*a^2)/2 + (3*C*b^2)/8))/(4*A*a^2 + 2*A*b^2 + 2*C*a^2 + (3*C*b^2)/2))*(2*A*a^2 + A*b^2 + C*a^2 + (3*C*b^2)/4))/d","B"
648,1,209,103,3.686636,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,C\,b^2\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a\,b\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}-\frac{A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}-\frac{C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*b^2*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (2*C*b^2*sin(c + d*x))/(3*d*cos(c + d*x)) + (C*b^2*sin(c + d*x))/(3*d*cos(c + d*x)^3) - (A*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d - (C*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (C*a*b*sin(c + d*x))/(d*cos(c + d*x)^2)","B"
649,1,188,109,4.233192,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{2\,\left(A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+2\,A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{2}+C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(A*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 2*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((A*a^2*sin(3*c + 3*d*x))/4 + (A*a^2*sin(c + d*x))/4 + (C*b^2*sin(c + d*x))/2 + C*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
650,1,193,103,3.770818,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{C\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}-\frac{A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}","Not used",1,"(C*b^2*sin(c + d*x))/(d*cos(c + d*x)) - (A*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (A*a^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d + (2*A*a*b*sin(c + d*x))/d - (C*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (A*a^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
651,1,170,112,3.808989,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{3\,A\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{2\,A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(3*A*a^2*sin(c + d*x))/(4*d) + (A*b^2*sin(c + d*x))/d + (C*a^2*sin(c + d*x))/d + (2*C*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^2*sin(3*c + 3*d*x))/(12*d) + (2*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*b*sin(2*c + 2*d*x))/(2*d)","B"
652,1,145,145,3.539087,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{3\,A\,a^2\,x}{8}+\frac{A\,b^2\,x}{2}+\frac{C\,a^2\,x}{2}+C\,b^2\,x+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,A\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{2\,C\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"(3*A*a^2*x)/8 + (A*b^2*x)/2 + (C*a^2*x)/2 + C*b^2*x + (A*a^2*sin(2*c + 2*d*x))/(4*d) + (A*a^2*sin(4*c + 4*d*x))/(32*d) + (A*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (3*A*a*b*sin(c + d*x))/(2*d) + (2*C*a*b*sin(c + d*x))/d + (A*a*b*sin(3*c + 3*d*x))/(6*d)","B"
653,1,342,161,6.335007,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2-\frac{5\,A\,a\,b}{2}-2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^2}{3}+\frac{16\,A\,b^2}{3}+\frac{16\,C\,a^2}{3}+8\,C\,b^2-A\,a\,b-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^2}{15}+\frac{20\,A\,b^2}{3}+\frac{20\,C\,a^2}{3}+12\,C\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^2}{3}+\frac{16\,A\,b^2}{3}+\frac{16\,C\,a^2}{3}+8\,C\,b^2+A\,a\,b+4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2+\frac{5\,A\,a\,b}{2}+2\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,C\right)}{2\,\left(\frac{3\,A\,a\,b}{2}+2\,C\,a\,b\right)}\right)\,\left(3\,A+4\,C\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 - (5*A*a*b)/2 - 2*C*a*b) + tan(c/2 + (d*x)/2)^3*((8*A*a^2)/3 + (16*A*b^2)/3 + (16*C*a^2)/3 + 8*C*b^2 + A*a*b + 4*C*a*b) + tan(c/2 + (d*x)/2)^7*((8*A*a^2)/3 + (16*A*b^2)/3 + (16*C*a^2)/3 + 8*C*b^2 - A*a*b - 4*C*a*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^2)/15 + (20*A*b^2)/3 + (20*C*a^2)/3 + 12*C*b^2) + tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 + (5*A*a*b)/2 + 2*C*a*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(3*A + 4*C))/(2*((3*A*a*b)/2 + 2*C*a*b)))*(3*A + 4*C))/(2*d)","B"
654,1,574,306,7.322856,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{\left(\frac{5\,A\,b^3}{4}-2\,A\,a^3-2\,C\,a^3+\frac{11\,C\,b^3}{8}-6\,A\,a\,b^2+3\,A\,a^2\,b-6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(10\,A\,a^3-\frac{7\,A\,b^3}{4}+\frac{22\,C\,a^3}{3}+\frac{5\,C\,b^3}{24}+22\,A\,a\,b^2-9\,A\,a^2\,b+14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b^3}{2}-20\,A\,a^3-12\,C\,a^3+\frac{15\,C\,b^3}{4}-36\,A\,a\,b^2+6\,A\,a^2\,b-\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(20\,A\,a^3+\frac{A\,b^3}{2}+12\,C\,a^3+\frac{15\,C\,b^3}{4}+36\,A\,a\,b^2+6\,A\,a^2\,b+\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,C\,b^3}{24}-\frac{7\,A\,b^3}{4}-\frac{22\,C\,a^3}{3}-10\,A\,a^3-22\,A\,a\,b^2-9\,A\,a^2\,b-14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+\frac{5\,A\,b^3}{4}+2\,C\,a^3+\frac{11\,C\,b^3}{8}+6\,A\,a\,b^2+3\,A\,a^2\,b+6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atanh}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,A\,a^2+6\,A\,b^2+18\,C\,a^2+5\,C\,b^2\right)}{4\,\left(\frac{3\,A\,b^3}{2}+\frac{5\,C\,b^3}{4}+6\,A\,a^2\,b+\frac{9\,C\,a^2\,b}{2}\right)}\right)\,\left(24\,A\,a^2+6\,A\,b^2+18\,C\,a^2+5\,C\,b^2\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^3 + (5*A*b^3)/4 + 2*C*a^3 + (11*C*b^3)/8 + 6*A*a*b^2 + 3*A*a^2*b + 6*C*a*b^2 + (15*C*a^2*b)/4) - tan(c/2 + (d*x)/2)^11*(2*A*a^3 - (5*A*b^3)/4 + 2*C*a^3 - (11*C*b^3)/8 + 6*A*a*b^2 - 3*A*a^2*b + 6*C*a*b^2 - (15*C*a^2*b)/4) - tan(c/2 + (d*x)/2)^3*(10*A*a^3 + (7*A*b^3)/4 + (22*C*a^3)/3 - (5*C*b^3)/24 + 22*A*a*b^2 + 9*A*a^2*b + 14*C*a*b^2 + (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^9*(10*A*a^3 - (7*A*b^3)/4 + (22*C*a^3)/3 + (5*C*b^3)/24 + 22*A*a*b^2 - 9*A*a^2*b + 14*C*a*b^2 - (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^5*(20*A*a^3 + (A*b^3)/2 + 12*C*a^3 + (15*C*b^3)/4 + 36*A*a*b^2 + 6*A*a^2*b + (156*C*a*b^2)/5 + (3*C*a^2*b)/2) - tan(c/2 + (d*x)/2)^7*(20*A*a^3 - (A*b^3)/2 + 12*C*a^3 - (15*C*b^3)/4 + 36*A*a*b^2 - 6*A*a^2*b + (156*C*a*b^2)/5 - (3*C*a^2*b)/2))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (b*atanh((b*tan(c/2 + (d*x)/2)*(24*A*a^2 + 6*A*b^2 + 18*C*a^2 + 5*C*b^2))/(4*((3*A*b^3)/2 + (5*C*b^3)/4 + 6*A*a^2*b + (9*C*a^2*b)/2)))*(24*A*a^2 + 6*A*b^2 + 18*C*a^2 + 5*C*b^2))/(8*d)","B"
655,1,445,234,7.519140,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3)/cos(c + d*x),x)","\frac{a\,\mathrm{atanh}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A\,a^2+12\,A\,b^2+4\,C\,a^2+9\,C\,b^2\right)}{2\,\left(4\,A\,a^3+2\,C\,a^3+6\,A\,a\,b^2+\frac{9\,C\,a\,b^2}{2}\right)}\right)\,\left(8\,A\,a^2+12\,A\,b^2+4\,C\,a^2+9\,C\,b^2\right)}{4\,d}-\frac{\left(2\,A\,b^3-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,C\,a^3-\frac{16\,A\,b^3}{3}-\frac{8\,C\,b^3}{3}+6\,A\,a\,b^2-24\,A\,a^2\,b+\frac{3\,C\,a\,b^2}{2}-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b^3}{3}+\frac{116\,C\,b^3}{15}+36\,A\,a^2\,b+20\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,A\,b^3}{3}-2\,C\,a^3-\frac{8\,C\,b^3}{3}-6\,A\,a\,b^2-24\,A\,a^2\,b-\frac{3\,C\,a\,b^2}{2}-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b^3+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b+\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh((a*tan(c/2 + (d*x)/2)*(8*A*a^2 + 12*A*b^2 + 4*C*a^2 + 9*C*b^2))/(2*(4*A*a^3 + 2*C*a^3 + 6*A*a*b^2 + (9*C*a*b^2)/2)))*(8*A*a^2 + 12*A*b^2 + 4*C*a^2 + 9*C*b^2))/(4*d) - (tan(c/2 + (d*x)/2)^9*(2*A*b^3 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b - (15*C*a*b^2)/4 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((16*A*b^3)/3 + 2*C*a^3 + (8*C*b^3)/3 + 6*A*a*b^2 + 24*A*a^2*b + (3*C*a*b^2)/2 + 16*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((16*A*b^3)/3 - 2*C*a^3 + (8*C*b^3)/3 - 6*A*a*b^2 + 24*A*a^2*b - (3*C*a*b^2)/2 + 16*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((20*A*b^3)/3 + (116*C*b^3)/15 + 36*A*a^2*b + 20*C*a^2*b) + tan(c/2 + (d*x)/2)*(2*A*b^3 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b + (15*C*a*b^2)/4 + 6*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
656,1,1547,167,6.029937,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\frac{3\,A\,a^3\,\mathrm{atan}\left(\frac{64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+192\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^6+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+240\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^6+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+72\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^6+576\,A^2\,a^4\,b^2+192\,A^2\,a^2\,b^4+16\,A^2\,b^6+576\,A\,C\,a^4\,b^2+240\,A\,C\,a^2\,b^4+24\,A\,C\,b^6+144\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4+9\,C^2\,b^6\right)}\right)}{4}+\frac{3\,A\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{9\,C\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32}+\frac{A\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{3\,C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{A\,b^3\,\sin\left(c+d\,x\right)}{8}+\frac{11\,C\,b^3\,\sin\left(c+d\,x\right)}{32}+\frac{3\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{8}+\frac{9\,A\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{9\,C\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{3\,A\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,A\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{8}+C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{4}+A\,a^3\,\mathrm{atan}\left(\frac{64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+192\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^6+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+240\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^6+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+72\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^6+576\,A^2\,a^4\,b^2+192\,A^2\,a^2\,b^4+16\,A^2\,b^6+576\,A\,C\,a^4\,b^2+240\,A\,C\,a^2\,b^4+24\,A\,C\,b^6+144\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4+9\,C^2\,b^6\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{A\,a^3\,\mathrm{atan}\left(\frac{64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+192\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^6+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+240\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^6+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+72\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^6+576\,A^2\,a^4\,b^2+192\,A^2\,a^2\,b^4+16\,A^2\,b^6+576\,A\,C\,a^4\,b^2+240\,A\,C\,a^2\,b^4+24\,A\,C\,b^6+144\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4+9\,C^2\,b^6\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}+\frac{A\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3\,C\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{8}+\frac{3\,C\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{32}+3\,A\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{3\,A\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,C\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((3*A*a^3*atan((64*A^2*a^6*sin(c/2 + (d*x)/2) + 16*A^2*b^6*sin(c/2 + (d*x)/2) + 9*C^2*b^6*sin(c/2 + (d*x)/2) + 192*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 576*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 72*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 144*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^6*sin(c/2 + (d*x)/2) + 240*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 576*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(64*A^2*a^6 + 16*A^2*b^6 + 9*C^2*b^6 + 192*A^2*a^2*b^4 + 576*A^2*a^4*b^2 + 72*C^2*a^2*b^4 + 144*C^2*a^4*b^2 + 24*A*C*b^6 + 240*A*C*a^2*b^4 + 576*A*C*a^4*b^2))))/4 + (3*A*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (9*C*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/32 + (A*b^3*sin(3*c + 3*d*x))/8 + (C*a^3*sin(2*c + 2*d*x))/4 + (C*a^3*sin(4*c + 4*d*x))/8 + (3*C*b^3*sin(3*c + 3*d*x))/32 + (A*b^3*sin(c + d*x))/8 + (11*C*b^3*sin(c + d*x))/32 + (3*C*a^2*b*sin(c + d*x))/8 + (9*A*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (9*C*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (3*A*a*b^2*sin(2*c + 2*d*x))/4 + (3*A*a*b^2*sin(4*c + 4*d*x))/8 + C*a*b^2*sin(2*c + 2*d*x) + (3*C*a^2*b*sin(3*c + 3*d*x))/8 + (C*a*b^2*sin(4*c + 4*d*x))/4 + A*a^3*atan((64*A^2*a^6*sin(c/2 + (d*x)/2) + 16*A^2*b^6*sin(c/2 + (d*x)/2) + 9*C^2*b^6*sin(c/2 + (d*x)/2) + 192*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 576*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 72*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 144*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^6*sin(c/2 + (d*x)/2) + 240*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 576*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(64*A^2*a^6 + 16*A^2*b^6 + 9*C^2*b^6 + 192*A^2*a^2*b^4 + 576*A^2*a^4*b^2 + 72*C^2*a^2*b^4 + 144*C^2*a^4*b^2 + 24*A*C*b^6 + 240*A*C*a^2*b^4 + 576*A*C*a^4*b^2)))*cos(2*c + 2*d*x) + (A*a^3*atan((64*A^2*a^6*sin(c/2 + (d*x)/2) + 16*A^2*b^6*sin(c/2 + (d*x)/2) + 9*C^2*b^6*sin(c/2 + (d*x)/2) + 192*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 576*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 72*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 144*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^6*sin(c/2 + (d*x)/2) + 240*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 576*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(64*A^2*a^6 + 16*A^2*b^6 + 9*C^2*b^6 + 192*A^2*a^2*b^4 + 576*A^2*a^4*b^2 + 72*C^2*a^2*b^4 + 144*C^2*a^4*b^2 + 24*A*C*b^6 + 240*A*C*a^2*b^4 + 576*A*C*a^4*b^2)))*cos(4*c + 4*d*x))/4 + (A*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (A*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8 + (3*C*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/8 + (3*C*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/32 + 3*A*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (3*A*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/4 + (3*C*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (3*C*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8)/(d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
657,1,464,167,5.373787,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{A\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{A\,b^3\,\sin\left(c+d\,x\right)}{4}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4}-\frac{C\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}+\frac{3\,A\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{A\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{2}-\frac{C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{4}+\frac{9\,A\,a^2\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{A\,a\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{2}-\frac{C\,a\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{4}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*a^3*sin(2*c + 2*d*x))/4 + (A*a^3*sin(4*c + 4*d*x))/8 + (A*b^3*sin(3*c + 3*d*x))/4 + (C*b^3*sin(3*c + 3*d*x))/6 + (A*b^3*sin(c + d*x))/4 + (C*b^3*sin(c + d*x))/2 + (3*C*a^2*b*sin(c + d*x))/4 - (C*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 + (3*C*a*b^2*sin(2*c + 2*d*x))/4 + (3*C*a^2*b*sin(3*c + 3*d*x))/4 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 + (3*A*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (A*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/2 - (C*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/4 + (9*A*a^2*b*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (A*a*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2 - (C*a*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/4)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
658,1,282,168,5.467723,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,\left(\frac{A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+A\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+3\,A\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+3\,C\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,A\,a^2\,b\,\sin\left(c+d\,x\right)}{4}+\frac{3\,A\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + A*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 3*A*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 3*C*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((A*a^3*sin(2*c + 2*d*x))/8 + (A*a^3*sin(4*c + 4*d*x))/16 + (C*b^3*sin(c + d*x))/2 + (3*A*a^2*b*sin(c + d*x))/4 + (3*A*a^2*b*sin(3*c + 3*d*x))/4 + (3*C*a*b^2*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
659,1,238,163,5.065419,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,A\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+3\,A\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+6\,C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}+\frac{\frac{5\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{24}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+C\,b^3\,\sin\left(c+d\,x\right)+\frac{3\,A\,a^2\,b\,\sin\left(c+d\,x\right)}{8}+\frac{3\,A\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,A\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{8}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*A*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 3*A*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*C*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - C*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/d + ((5*A*a^3*sin(2*c + 2*d*x))/12 + (A*a^3*sin(4*c + 4*d*x))/24 + (C*a^3*sin(2*c + 2*d*x))/2 + C*b^3*sin(c + d*x) + (3*A*a^2*b*sin(c + d*x))/8 + (3*A*a*b^2*sin(2*c + 2*d*x))/2 + (3*A*a^2*b*sin(3*c + 3*d*x))/8)/(d*cos(c + d*x))","B"
660,1,2008,182,5.786323,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\left(2\,A\,b^3-\frac{5\,A\,a^3}{4}-C\,a^3-3\,A\,a\,b^2+6\,A\,a^2\,b+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a^3}{4}+6\,A\,b^3-C\,a^3-3\,A\,a\,b^2+10\,A\,a^2\,b+18\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,b^3-\frac{3\,A\,a^3}{4}+C\,a^3+3\,A\,a\,b^2+10\,A\,a^2\,b+18\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a^3}{4}+2\,A\,b^3+C\,a^3+3\,A\,a\,b^2+6\,A\,a^2\,b+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{C\,b^3\,\mathrm{atan}\left(\frac{C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}}{576\,C^3\,a^2\,b^7-192\,C^3\,a\,b^8-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\right)-C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\right)-96\,A\,C^2\,a\,b^8+576\,A\,C^2\,a^2\,b^7-24\,A\,C^2\,a^3\,b^6+240\,A\,C^2\,a^4\,b^5+24\,A\,C^2\,a^6\,b^3+144\,A^2\,C\,a^2\,b^7+72\,A^2\,C\,a^4\,b^5+9\,A^2\,C\,a^6\,b^3}\right)\,2{}\mathrm{i}}{d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-\frac{a\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\,1{}\mathrm{i}}{8}\right)\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)}{8}+\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+\frac{a\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\,1{}\mathrm{i}}{8}\right)\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)}{8}}{576\,C^3\,a^2\,b^7-192\,C^3\,a\,b^8-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3-96\,A\,C^2\,a\,b^8+576\,A\,C^2\,a^2\,b^7-24\,A\,C^2\,a^3\,b^6+240\,A\,C^2\,a^4\,b^5+24\,A\,C^2\,a^6\,b^3+144\,A^2\,C\,a^2\,b^7+72\,A^2\,C\,a^4\,b^5+9\,A^2\,C\,a^6\,b^3-\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-\frac{a\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\,1{}\mathrm{i}}{8}\right)\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)\,1{}\mathrm{i}}{8}+\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+\frac{a\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)\,\left(12\,A\,a^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+96\,C\,a\,b^2\right)\,1{}\mathrm{i}}{8}\right)\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)\,1{}\mathrm{i}}{8}}\right)\,\left(3\,A\,a^2+12\,A\,b^2+4\,C\,a^2+24\,C\,b^2\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*a^3)/4 + 2*A*b^3 + C*a^3 + 3*A*a*b^2 + 6*A*a^2*b + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((5*A*a^3)/4 - 2*A*b^3 + C*a^3 + 3*A*a*b^2 - 6*A*a^2*b - 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(6*A*b^3 - (3*A*a^3)/4 + C*a^3 + 3*A*a*b^2 + 10*A*a^2*b + 18*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((3*A*a^3)/4 + 6*A*b^3 - C*a^3 - 3*A*a*b^2 + 10*A*a^2*b + 18*C*a^2*b))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (C*b^3*atan((C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) + C*b^3*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2))*1i + C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) - C*b^3*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2))*1i)/(576*C^3*a^2*b^7 - 192*C^3*a*b^8 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 + C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) + C*b^3*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2)) - C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) - C*b^3*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2)) - 96*A*C^2*a*b^8 + 576*A*C^2*a^2*b^7 - 24*A*C^2*a^3*b^6 + 240*A*C^2*a^4*b^5 + 24*A*C^2*a^6*b^3 + 144*A^2*C*a^2*b^7 + 72*A^2*C*a^4*b^5 + 9*A^2*C*a^6*b^3))*2i)/d - (a*atan(((a*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) - (a*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2)*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2)*1i)/8)*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2))/8 + (a*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) + (a*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2)*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2)*1i)/8)*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2))/8)/((a*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) + (a*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2)*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2)*1i)/8)*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2)*1i)/8 - (a*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2) - (a*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2)*(12*A*a^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 96*C*a*b^2)*1i)/8)*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2)*1i)/8 - 192*C^3*a*b^8 + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 - 96*A*C^2*a*b^8 + 576*A*C^2*a^2*b^7 - 24*A*C^2*a^3*b^6 + 240*A*C^2*a^4*b^5 + 24*A*C^2*a^6*b^3 + 144*A^2*C*a^2*b^7 + 72*A^2*C*a^4*b^5 + 9*A^2*C*a^6*b^3))*(3*A*a^2 + 12*A*b^2 + 4*C*a^2 + 24*C*b^2))/(4*d)","B"
661,1,442,218,6.901247,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\left(2\,A\,a^3-A\,b^3+2\,C\,a^3+6\,A\,a\,b^2-\frac{15\,A\,a^2\,b}{4}+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^3}{3}-2\,A\,b^3+\frac{16\,C\,a^3}{3}+16\,A\,a\,b^2-\frac{3\,A\,a^2\,b}{2}+24\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^3}{15}+\frac{20\,C\,a^3}{3}+20\,A\,a\,b^2+36\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^3}{3}+2\,A\,b^3+\frac{16\,C\,a^3}{3}+16\,A\,a\,b^2+\frac{3\,A\,a^2\,b}{2}+24\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+A\,b^3+2\,C\,a^3+6\,A\,a\,b^2+\frac{15\,A\,a^2\,b}{4}+6\,C\,a\,b^2+3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A\,a^2+4\,A\,b^2+12\,C\,a^2+8\,C\,b^2\right)}{4\,\left(A\,b^3+2\,C\,b^3+\frac{9\,A\,a^2\,b}{4}+3\,C\,a^2\,b\right)}\right)\,\left(9\,A\,a^2+4\,A\,b^2+12\,C\,a^2+8\,C\,b^2\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(2*A*a^3 - A*b^3 + 2*C*a^3 + 6*A*a*b^2 - (15*A*a^2*b)/4 + 6*C*a*b^2 - 3*C*a^2*b) + tan(c/2 + (d*x)/2)^3*((8*A*a^3)/3 + 2*A*b^3 + (16*C*a^3)/3 + 16*A*a*b^2 + (3*A*a^2*b)/2 + 24*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^7*((8*A*a^3)/3 - 2*A*b^3 + (16*C*a^3)/3 + 16*A*a*b^2 - (3*A*a^2*b)/2 + 24*C*a*b^2 - 6*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^3)/15 + (20*C*a^3)/3 + 20*A*a*b^2 + 36*C*a*b^2) + tan(c/2 + (d*x)/2)*(2*A*a^3 + A*b^3 + 2*C*a^3 + 6*A*a*b^2 + (15*A*a^2*b)/4 + 6*C*a*b^2 + 3*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (b*atan((b*tan(c/2 + (d*x)/2)*(9*A*a^2 + 4*A*b^2 + 12*C*a^2 + 8*C*b^2))/(4*(A*b^3 + 2*C*b^3 + (9*A*a^2*b)/4 + 3*C*a^2*b)))*(9*A*a^2 + 4*A*b^2 + 12*C*a^2 + 8*C*b^2))/(4*d)","B"
662,1,573,257,6.782870,"\text{Not used}","int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\left(2\,A\,b^3-\frac{11\,A\,a^3}{8}-\frac{5\,C\,a^3}{4}+2\,C\,b^3-\frac{15\,A\,a\,b^2}{4}+6\,A\,a^2\,b-3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,A\,a^3}{24}+\frac{22\,A\,b^3}{3}-\frac{7\,C\,a^3}{4}+10\,C\,b^3-\frac{21\,A\,a\,b^2}{4}+14\,A\,a^2\,b-9\,C\,a\,b^2+22\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(12\,A\,b^3-\frac{15\,A\,a^3}{4}-\frac{C\,a^3}{2}+20\,C\,b^3-\frac{3\,A\,a\,b^2}{2}+\frac{156\,A\,a^2\,b}{5}-6\,C\,a\,b^2+36\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,A\,a^3}{4}+12\,A\,b^3+\frac{C\,a^3}{2}+20\,C\,b^3+\frac{3\,A\,a\,b^2}{2}+\frac{156\,A\,a^2\,b}{5}+6\,C\,a\,b^2+36\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{22\,A\,b^3}{3}-\frac{5\,A\,a^3}{24}+\frac{7\,C\,a^3}{4}+10\,C\,b^3+\frac{21\,A\,a\,b^2}{4}+14\,A\,a^2\,b+9\,C\,a\,b^2+22\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,A\,a^3}{8}+2\,A\,b^3+\frac{5\,C\,a^3}{4}+2\,C\,b^3+\frac{15\,A\,a\,b^2}{4}+6\,A\,a^2\,b+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^2+18\,A\,b^2+6\,C\,a^2+24\,C\,b^2\right)}{8\,\left(\frac{5\,A\,a^3}{8}+\frac{3\,C\,a^3}{4}+\frac{9\,A\,a\,b^2}{4}+3\,C\,a\,b^2\right)}\right)\,\left(5\,A\,a^2+18\,A\,b^2+6\,C\,a^2+24\,C\,b^2\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((11*A*a^3)/8 + 2*A*b^3 + (5*C*a^3)/4 + 2*C*b^3 + (15*A*a*b^2)/4 + 6*A*a^2*b + 3*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^11*((11*A*a^3)/8 - 2*A*b^3 + (5*C*a^3)/4 - 2*C*b^3 + (15*A*a*b^2)/4 - 6*A*a^2*b + 3*C*a*b^2 - 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*((22*A*b^3)/3 - (5*A*a^3)/24 + (7*C*a^3)/4 + 10*C*b^3 + (21*A*a*b^2)/4 + 14*A*a^2*b + 9*C*a*b^2 + 22*C*a^2*b) + tan(c/2 + (d*x)/2)^9*((5*A*a^3)/24 + (22*A*b^3)/3 - (7*C*a^3)/4 + 10*C*b^3 - (21*A*a*b^2)/4 + 14*A*a^2*b - 9*C*a*b^2 + 22*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((15*A*a^3)/4 + 12*A*b^3 + (C*a^3)/2 + 20*C*b^3 + (3*A*a*b^2)/2 + (156*A*a^2*b)/5 + 6*C*a*b^2 + 36*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((15*A*a^3)/4 - 12*A*b^3 + (C*a^3)/2 - 20*C*b^3 + (3*A*a*b^2)/2 - (156*A*a^2*b)/5 + 6*C*a*b^2 - 36*C*a^2*b))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(5*A*a^2 + 18*A*b^2 + 6*C*a^2 + 24*C*b^2))/(8*((5*A*a^3)/8 + (3*C*a^3)/4 + (9*A*a*b^2)/4 + 3*C*a*b^2)))*(5*A*a^2 + 18*A*b^2 + 6*C*a^2 + 24*C*b^2))/(8*d)","B"
663,1,755,381,7.726299,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4)/cos(c + d*x)^2,x)","\frac{a\,b\,\mathrm{atanh}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A\,a^2+6\,A\,b^2+6\,C\,a^2+5\,C\,b^2\right)}{6\,A\,a\,b^3+8\,A\,a^3\,b+5\,C\,a\,b^3+6\,C\,a^3\,b}\right)\,\left(8\,A\,a^2+6\,A\,b^2+6\,C\,a^2+5\,C\,b^2\right)}{2\,d}-\frac{\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2-5\,A\,a\,b^3-4\,A\,a^3\,b-\frac{11\,C\,a\,b^3}{2}-5\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(12\,A\,a\,b^3-\frac{20\,A\,b^4}{3}-\frac{28\,C\,a^4}{3}-4\,C\,b^4-56\,A\,a^2\,b^2-40\,C\,a^2\,b^2-12\,A\,a^4+16\,A\,a^3\,b+\frac{14\,C\,a\,b^3}{3}+12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(30\,A\,a^4+\frac{226\,A\,b^4}{15}+\frac{58\,C\,a^4}{3}+\frac{86\,C\,b^4}{5}+116\,A\,a^2\,b^2+\frac{452\,C\,a^2\,b^2}{5}-9\,A\,a\,b^3-20\,A\,a^3\,b-\frac{85\,C\,a\,b^3}{6}-9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-40\,A\,a^4-\frac{104\,A\,b^4}{5}-24\,C\,a^4-\frac{424\,C\,b^4}{35}-144\,A\,a^2\,b^2-\frac{624\,C\,a^2\,b^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(30\,A\,a^4+\frac{226\,A\,b^4}{15}+\frac{58\,C\,a^4}{3}+\frac{86\,C\,b^4}{5}+116\,A\,a^2\,b^2+\frac{452\,C\,a^2\,b^2}{5}+9\,A\,a\,b^3+20\,A\,a^3\,b+\frac{85\,C\,a\,b^3}{6}+9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-12\,A\,a^4-\frac{20\,A\,b^4}{3}-\frac{28\,C\,a^4}{3}-4\,C\,b^4-56\,A\,a^2\,b^2-40\,C\,a^2\,b^2-12\,A\,a\,b^3-16\,A\,a^3\,b-\frac{14\,C\,a\,b^3}{3}-12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2+5\,A\,a\,b^3+4\,A\,a^3\,b+\frac{11\,C\,a\,b^3}{2}+5\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*b*atanh((a*b*tan(c/2 + (d*x)/2)*(8*A*a^2 + 6*A*b^2 + 6*C*a^2 + 5*C*b^2))/(6*A*a*b^3 + 8*A*a^3*b + 5*C*a*b^3 + 6*C*a^3*b))*(8*A*a^2 + 6*A*b^2 + 6*C*a^2 + 5*C*b^2))/(2*d) - (tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 + 5*A*a*b^3 + 4*A*a^3*b + (11*C*a*b^3)/2 + 5*C*a^3*b) - tan(c/2 + (d*x)/2)^7*(40*A*a^4 + (104*A*b^4)/5 + 24*C*a^4 + (424*C*b^4)/35 + 144*A*a^2*b^2 + (624*C*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^13*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 - 5*A*a*b^3 - 4*A*a^3*b - (11*C*a*b^3)/2 - 5*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(12*A*a^4 + (20*A*b^4)/3 + (28*C*a^4)/3 + 4*C*b^4 + 56*A*a^2*b^2 + 40*C*a^2*b^2 + 12*A*a*b^3 + 16*A*a^3*b + (14*C*a*b^3)/3 + 12*C*a^3*b) - tan(c/2 + (d*x)/2)^11*(12*A*a^4 + (20*A*b^4)/3 + (28*C*a^4)/3 + 4*C*b^4 + 56*A*a^2*b^2 + 40*C*a^2*b^2 - 12*A*a*b^3 - 16*A*a^3*b - (14*C*a*b^3)/3 - 12*C*a^3*b) + tan(c/2 + (d*x)/2)^5*(30*A*a^4 + (226*A*b^4)/15 + (58*C*a^4)/3 + (86*C*b^4)/5 + 116*A*a^2*b^2 + (452*C*a^2*b^2)/5 + 9*A*a*b^3 + 20*A*a^3*b + (85*C*a*b^3)/6 + 9*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(30*A*a^4 + (226*A*b^4)/15 + (58*C*a^4)/3 + (86*C*b^4)/5 + 116*A*a^2*b^2 + (452*C*a^2*b^2)/5 - 9*A*a*b^3 - 20*A*a^3*b - (85*C*a*b^3)/6 - 9*C*a^3*b))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
664,1,690,310,6.596461,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4)/cos(c + d*x),x)","\frac{\left(\frac{5\,A\,b^4}{4}+C\,a^4+\frac{11\,C\,b^4}{8}+6\,A\,a^2\,b^2+\frac{15\,C\,a^2\,b^2}{2}-8\,A\,a\,b^3-8\,A\,a^3\,b-8\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,C\,b^4}{24}-3\,C\,a^4-\frac{7\,A\,b^4}{4}-18\,A\,a^2\,b^2-\frac{21\,C\,a^2\,b^2}{2}+\frac{88\,A\,a\,b^3}{3}+40\,A\,a^3\,b+\frac{56\,C\,a\,b^3}{3}+\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b^4}{2}+2\,C\,a^4+\frac{15\,C\,b^4}{4}+12\,A\,a^2\,b^2+3\,C\,a^2\,b^2-48\,A\,a\,b^3-80\,A\,a^3\,b-\frac{208\,C\,a\,b^3}{5}-48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{A\,b^4}{2}+2\,C\,a^4+\frac{15\,C\,b^4}{4}+12\,A\,a^2\,b^2+3\,C\,a^2\,b^2+48\,A\,a\,b^3+80\,A\,a^3\,b+\frac{208\,C\,a\,b^3}{5}+48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,C\,b^4}{24}-3\,C\,a^4-\frac{7\,A\,b^4}{4}-18\,A\,a^2\,b^2-\frac{21\,C\,a^2\,b^2}{2}-\frac{88\,A\,a\,b^3}{3}-40\,A\,a^3\,b-\frac{56\,C\,a\,b^3}{3}-\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,b^4}{4}+C\,a^4+\frac{11\,C\,b^4}{8}+6\,A\,a^2\,b^2+\frac{15\,C\,a^2\,b^2}{2}+8\,A\,a\,b^3+8\,A\,a^3\,b+8\,C\,a\,b^3+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^4+\frac{3\,A\,b^4}{8}+\frac{C\,a^4}{2}+\frac{5\,C\,b^4}{16}+3\,A\,a^2\,b^2+\frac{9\,C\,a^2\,b^2}{4}\right)}{4\,A\,a^4+\frac{3\,A\,b^4}{2}+2\,C\,a^4+\frac{5\,C\,b^4}{4}+12\,A\,a^2\,b^2+9\,C\,a^2\,b^2}\right)\,\left(2\,A\,a^4+\frac{3\,A\,b^4}{4}+C\,a^4+\frac{5\,C\,b^4}{8}+6\,A\,a^2\,b^2+\frac{9\,C\,a^2\,b^2}{2}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*b^4)/4 + C*a^4 + (11*C*b^4)/8 + 6*A*a^2*b^2 + (15*C*a^2*b^2)/2 + 8*A*a*b^3 + 8*A*a^3*b + 8*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^11*((5*A*b^4)/4 + C*a^4 + (11*C*b^4)/8 + 6*A*a^2*b^2 + (15*C*a^2*b^2)/2 - 8*A*a*b^3 - 8*A*a^3*b - 8*C*a*b^3 - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^3*((7*A*b^4)/4 + 3*C*a^4 - (5*C*b^4)/24 + 18*A*a^2*b^2 + (21*C*a^2*b^2)/2 + (88*A*a*b^3)/3 + 40*A*a^3*b + (56*C*a*b^3)/3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^9*((5*C*b^4)/24 - 3*C*a^4 - (7*A*b^4)/4 - 18*A*a^2*b^2 - (21*C*a^2*b^2)/2 + (88*A*a*b^3)/3 + 40*A*a^3*b + (56*C*a*b^3)/3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^5*((A*b^4)/2 + 2*C*a^4 + (15*C*b^4)/4 + 12*A*a^2*b^2 + 3*C*a^2*b^2 + 48*A*a*b^3 + 80*A*a^3*b + (208*C*a*b^3)/5 + 48*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((A*b^4)/2 + 2*C*a^4 + (15*C*b^4)/4 + 12*A*a^2*b^2 + 3*C*a^2*b^2 - 48*A*a*b^3 - 80*A*a^3*b - (208*C*a*b^3)/5 - 48*C*a^3*b))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*(A*a^4 + (3*A*b^4)/8 + (C*a^4)/2 + (5*C*b^4)/16 + 3*A*a^2*b^2 + (9*C*a^2*b^2)/4))/(4*A*a^4 + (3*A*b^4)/2 + 2*C*a^4 + (5*C*b^4)/4 + 12*A*a^2*b^2 + 9*C*a^2*b^2))*(2*A*a^4 + (3*A*b^4)/4 + C*a^4 + (5*C*b^4)/8 + 6*A*a^2*b^2 + (9*C*a^2*b^2)/2))/d","B"
665,1,1738,227,6.508267,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{\frac{5\,A\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{24}+\frac{A\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{24}+\frac{3\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{16}+\frac{C\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{C\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{30}+\frac{A\,b^4\,\sin\left(c+d\,x\right)}{6}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{8}+\frac{C\,b^4\,\sin\left(c+d\,x\right)}{3}+\frac{5\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+80\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6+64\,A^2\,a^4\,b^2+64\,A^2\,a^2\,b^4+16\,A^2\,b^6+64\,A\,C\,a^4\,b^2+80\,A\,C\,a^2\,b^4+24\,A\,C\,b^6+16\,C^2\,a^4\,b^2+24\,C^2\,a^2\,b^4+9\,C^2\,b^6\right)}\right)}{4}+\frac{A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{3\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{7\,C\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{C\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,C\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{C\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{4}+C\,a^2\,b^2\,\sin\left(c+d\,x\right)+\frac{5\,A\,a^4\,\mathrm{atan}\left(\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+80\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6+64\,A^2\,a^4\,b^2+64\,A^2\,a^2\,b^4+16\,A^2\,b^6+64\,A\,C\,a^4\,b^2+80\,A\,C\,a^2\,b^4+24\,A\,C\,b^6+16\,C^2\,a^4\,b^2+24\,C^2\,a^2\,b^4+9\,C^2\,b^6\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}+\frac{A\,a^4\,\mathrm{atan}\left(\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+80\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6+64\,A^2\,a^4\,b^2+64\,A^2\,a^2\,b^4+16\,A^2\,b^6+64\,A\,C\,a^4\,b^2+80\,A\,C\,a^2\,b^4+24\,A\,C\,b^6+16\,C^2\,a^4\,b^2+24\,C^2\,a^2\,b^4+9\,C^2\,b^6\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{8}+\frac{9\,A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{3\,A\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{8}+\frac{5\,C\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{4}+\frac{5\,A\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{5\,A\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{A\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}+\frac{A\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{2}+\frac{15\,C\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{5\,C\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{16}+\frac{C\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}+\frac{5\,A\,a\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+5\,A\,a^3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{15\,C\,a\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{5\,C\,a^3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}}{d\,\left(\frac{5\,\cos\left(c+d\,x\right)}{8}+\frac{5\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{\cos\left(5\,c+5\,d\,x\right)}{16}\right)}","Not used",1,"((5*A*b^4*sin(3*c + 3*d*x))/24 + (A*b^4*sin(5*c + 5*d*x))/24 + (3*C*a^4*sin(3*c + 3*d*x))/16 + (C*a^4*sin(5*c + 5*d*x))/16 + (C*b^4*sin(3*c + 3*d*x))/6 + (C*b^4*sin(5*c + 5*d*x))/30 + (A*b^4*sin(c + d*x))/6 + (C*a^4*sin(c + d*x))/8 + (C*b^4*sin(c + d*x))/3 + (5*A*a^4*cos(c + d*x)*atan((4*A^2*a^6*sin(c/2 + (d*x)/2) + 16*A^2*b^6*sin(c/2 + (d*x)/2) + 9*C^2*b^6*sin(c/2 + (d*x)/2) + 64*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 64*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 16*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^6*sin(c/2 + (d*x)/2) + 80*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 64*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(4*A^2*a^6 + 16*A^2*b^6 + 9*C^2*b^6 + 64*A^2*a^2*b^4 + 64*A^2*a^4*b^2 + 24*C^2*a^2*b^4 + 16*C^2*a^4*b^2 + 24*A*C*b^6 + 80*A*C*a^2*b^4 + 64*A*C*a^4*b^2))))/4 + (A*a*b^3*sin(2*c + 2*d*x))/2 + (A*a*b^3*sin(4*c + 4*d*x))/4 + (3*A*a^2*b^2*sin(c + d*x))/4 + (7*C*a*b^3*sin(2*c + 2*d*x))/8 + (C*a^3*b*sin(2*c + 2*d*x))/2 + (3*C*a*b^3*sin(4*c + 4*d*x))/16 + (C*a^3*b*sin(4*c + 4*d*x))/4 + C*a^2*b^2*sin(c + d*x) + (5*A*a^4*atan((4*A^2*a^6*sin(c/2 + (d*x)/2) + 16*A^2*b^6*sin(c/2 + (d*x)/2) + 9*C^2*b^6*sin(c/2 + (d*x)/2) + 64*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 64*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 16*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^6*sin(c/2 + (d*x)/2) + 80*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 64*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(4*A^2*a^6 + 16*A^2*b^6 + 9*C^2*b^6 + 64*A^2*a^2*b^4 + 64*A^2*a^4*b^2 + 24*C^2*a^2*b^4 + 16*C^2*a^4*b^2 + 24*A*C*b^6 + 80*A*C*a^2*b^4 + 64*A*C*a^4*b^2)))*cos(3*c + 3*d*x))/8 + (A*a^4*atan((4*A^2*a^6*sin(c/2 + (d*x)/2) + 16*A^2*b^6*sin(c/2 + (d*x)/2) + 9*C^2*b^6*sin(c/2 + (d*x)/2) + 64*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 64*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 16*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^6*sin(c/2 + (d*x)/2) + 80*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 64*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(4*A^2*a^6 + 16*A^2*b^6 + 9*C^2*b^6 + 64*A^2*a^2*b^4 + 64*A^2*a^4*b^2 + 24*C^2*a^2*b^4 + 16*C^2*a^4*b^2 + 24*A*C*b^6 + 80*A*C*a^2*b^4 + 64*A*C*a^4*b^2)))*cos(5*c + 5*d*x))/8 + (9*A*a^2*b^2*sin(3*c + 3*d*x))/8 + (3*A*a^2*b^2*sin(5*c + 5*d*x))/8 + (5*C*a^2*b^2*sin(3*c + 3*d*x))/4 + (C*a^2*b^2*sin(5*c + 5*d*x))/4 + (5*A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (5*A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4 + (A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/2 + (15*C*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/16 + (5*C*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (3*C*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/16 + (C*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4 + (5*A*a*b^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 5*A*a^3*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (15*C*a*b^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (5*C*a^3*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2)/(d*((5*cos(c + d*x))/8 + (5*cos(3*c + 3*d*x))/16 + cos(5*c + 5*d*x)/16))","B"
666,1,1988,229,6.554939,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{\frac{9\,A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+9\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{27\,C\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{9\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{4}+\frac{3\,A\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{9\,C\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{3\,A\,a^4\,\sin\left(c+d\,x\right)}{2}+\frac{3\,A\,b^4\,\sin\left(c+d\,x\right)}{2}+\frac{33\,C\,b^4\,\sin\left(c+d\,x\right)}{8}+12\,A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+6\,A\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)+16\,C\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+12\,C\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+4\,C\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)+6\,C\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)+9\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)+36\,A\,a^3\,b\,\mathrm{atan}\left(\frac{1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+2304\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8+768\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+480\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^8+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^8}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1024\,A^2\,a^6\,b^2+2304\,A^2\,a^4\,b^4+384\,A^2\,a^2\,b^6+16\,A^2\,b^8+768\,A\,C\,a^6\,b^2+2368\,A\,C\,a^4\,b^4+480\,A\,C\,a^2\,b^6+24\,A\,C\,b^8+64\,C^2\,a^8+384\,C^2\,a^6\,b^2+624\,C^2\,a^4\,b^4+144\,C^2\,a^2\,b^6+9\,C^2\,b^8\right)}\right)+54\,A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+6\,A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{3\,A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{2}+12\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+3\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+27\,C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{9\,C\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{9\,C\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+9\,C\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)+48\,A\,a^3\,b\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+2304\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8+768\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+480\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^8+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^8}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1024\,A^2\,a^6\,b^2+2304\,A^2\,a^4\,b^4+384\,A^2\,a^2\,b^6+16\,A^2\,b^8+768\,A\,C\,a^6\,b^2+2368\,A\,C\,a^4\,b^4+480\,A\,C\,a^2\,b^6+24\,A\,C\,b^8+64\,C^2\,a^8+384\,C^2\,a^6\,b^2+624\,C^2\,a^4\,b^4+144\,C^2\,a^2\,b^6+9\,C^2\,b^8\right)}\right)+12\,A\,a^3\,b\,\cos\left(4\,c+4\,d\,x\right)\,\mathrm{atan}\left(\frac{1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+2304\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8+768\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+480\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,b^8+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^8}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1024\,A^2\,a^6\,b^2+2304\,A^2\,a^4\,b^4+384\,A^2\,a^2\,b^6+16\,A^2\,b^8+768\,A\,C\,a^6\,b^2+2368\,A\,C\,a^4\,b^4+480\,A\,C\,a^2\,b^6+24\,A\,C\,b^8+64\,C^2\,a^8+384\,C^2\,a^6\,b^2+624\,C^2\,a^4\,b^4+144\,C^2\,a^2\,b^6+9\,C^2\,b^8\right)}\right)+72\,A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+18\,A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+36\,C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+9\,C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{12\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((9*A*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 9*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (27*C*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (9*A*a^4*sin(3*c + 3*d*x))/4 + (3*A*a^4*sin(5*c + 5*d*x))/4 + (3*A*b^4*sin(3*c + 3*d*x))/2 + (9*C*b^4*sin(3*c + 3*d*x))/8 + (3*A*a^4*sin(c + d*x))/2 + (3*A*b^4*sin(c + d*x))/2 + (33*C*b^4*sin(c + d*x))/8 + 12*A*a*b^3*sin(2*c + 2*d*x) + 6*A*a*b^3*sin(4*c + 4*d*x) + 16*C*a*b^3*sin(2*c + 2*d*x) + 12*C*a^3*b*sin(2*c + 2*d*x) + 4*C*a*b^3*sin(4*c + 4*d*x) + 6*C*a^3*b*sin(4*c + 4*d*x) + 9*C*a^2*b^2*sin(c + d*x) + 36*A*a^3*b*atan((16*A^2*b^8*sin(c/2 + (d*x)/2) + 64*C^2*a^8*sin(c/2 + (d*x)/2) + 9*C^2*b^8*sin(c/2 + (d*x)/2) + 384*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 2304*A^2*a^4*b^4*sin(c/2 + (d*x)/2) + 1024*A^2*a^6*b^2*sin(c/2 + (d*x)/2) + 144*C^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*C^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*C^2*a^6*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^8*sin(c/2 + (d*x)/2) + 480*A*C*a^2*b^6*sin(c/2 + (d*x)/2) + 2368*A*C*a^4*b^4*sin(c/2 + (d*x)/2) + 768*A*C*a^6*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(16*A^2*b^8 + 64*C^2*a^8 + 9*C^2*b^8 + 384*A^2*a^2*b^6 + 2304*A^2*a^4*b^4 + 1024*A^2*a^6*b^2 + 144*C^2*a^2*b^6 + 624*C^2*a^4*b^4 + 384*C^2*a^6*b^2 + 24*A*C*b^8 + 480*A*C*a^2*b^6 + 2368*A*C*a^4*b^4 + 768*A*C*a^6*b^2))) + 54*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*A*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (3*A*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 + 12*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 3*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 27*C*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (9*C*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (9*C*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8 + 9*C*a^2*b^2*sin(3*c + 3*d*x) + 48*A*a^3*b*cos(2*c + 2*d*x)*atan((16*A^2*b^8*sin(c/2 + (d*x)/2) + 64*C^2*a^8*sin(c/2 + (d*x)/2) + 9*C^2*b^8*sin(c/2 + (d*x)/2) + 384*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 2304*A^2*a^4*b^4*sin(c/2 + (d*x)/2) + 1024*A^2*a^6*b^2*sin(c/2 + (d*x)/2) + 144*C^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*C^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*C^2*a^6*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^8*sin(c/2 + (d*x)/2) + 480*A*C*a^2*b^6*sin(c/2 + (d*x)/2) + 2368*A*C*a^4*b^4*sin(c/2 + (d*x)/2) + 768*A*C*a^6*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(16*A^2*b^8 + 64*C^2*a^8 + 9*C^2*b^8 + 384*A^2*a^2*b^6 + 2304*A^2*a^4*b^4 + 1024*A^2*a^6*b^2 + 144*C^2*a^2*b^6 + 624*C^2*a^4*b^4 + 384*C^2*a^6*b^2 + 24*A*C*b^8 + 480*A*C*a^2*b^6 + 2368*A*C*a^4*b^4 + 768*A*C*a^6*b^2))) + 12*A*a^3*b*cos(4*c + 4*d*x)*atan((16*A^2*b^8*sin(c/2 + (d*x)/2) + 64*C^2*a^8*sin(c/2 + (d*x)/2) + 9*C^2*b^8*sin(c/2 + (d*x)/2) + 384*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 2304*A^2*a^4*b^4*sin(c/2 + (d*x)/2) + 1024*A^2*a^6*b^2*sin(c/2 + (d*x)/2) + 144*C^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*C^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*C^2*a^6*b^2*sin(c/2 + (d*x)/2) + 24*A*C*b^8*sin(c/2 + (d*x)/2) + 480*A*C*a^2*b^6*sin(c/2 + (d*x)/2) + 2368*A*C*a^4*b^4*sin(c/2 + (d*x)/2) + 768*A*C*a^6*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(16*A^2*b^8 + 64*C^2*a^8 + 9*C^2*b^8 + 384*A^2*a^2*b^6 + 2304*A^2*a^4*b^4 + 1024*A^2*a^6*b^2 + 144*C^2*a^2*b^6 + 624*C^2*a^4*b^4 + 384*C^2*a^6*b^2 + 24*A*C*b^8 + 480*A*C*a^2*b^6 + 2368*A*C*a^4*b^4 + 768*A*C*a^6*b^2))) + 72*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 18*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 36*C*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 9*C*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/(12*d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
667,1,2664,219,5.897787,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","-\frac{\left(A\,a^4+2\,A\,b^4+2\,C\,b^4+12\,C\,a^2\,b^2-8\,A\,a^3\,b-4\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-4\,A\,a^4+16\,A\,a^3\,b-8\,C\,a\,b^3+\frac{8\,C\,b^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a^4-4\,A\,b^4+\frac{4\,C\,b^4}{3}-24\,C\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a^4-16\,A\,a^3\,b+8\,C\,a\,b^3+\frac{8\,C\,b^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a^4+2\,A\,b^4+2\,C\,b^4+12\,C\,a^2\,b^2+8\,A\,a^3\,b+4\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{a^2\,\mathrm{atan}\left(-\frac{\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)}{2}+\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)}{2}}{256\,C^3\,a^{11}\,b-6144\,A^3\,a^4\,b^8+9216\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+1536\,A^3\,a^7\,b^5+64\,A^3\,a^9\,b^3-256\,C^3\,a^6\,b^6-1024\,C^3\,a^8\,b^4+128\,C^3\,a^9\,b^3-1024\,C^3\,a^{10}\,b^2+256\,A\,C^2\,a^{11}\,b+64\,A^2\,C\,a^{11}\,b-1536\,A\,C^2\,a^4\,b^8-7296\,A\,C^2\,a^6\,b^6+1536\,A\,C^2\,a^7\,b^5-8704\,A\,C^2\,a^8\,b^4+3456\,A\,C^2\,a^9\,b^3-512\,A\,C^2\,a^{10}\,b^2-6144\,A^2\,C\,a^4\,b^8+4608\,A^2\,C\,a^5\,b^7-13824\,A^2\,C\,a^6\,b^6+13056\,A^2\,C\,a^7\,b^5-1024\,A^2\,C\,a^8\,b^4+1824\,A^2\,C\,a^9\,b^3-\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)\,1{}\mathrm{i}}{2}+\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)\,1{}\mathrm{i}}{2}}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2\right)}{d}-\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-2\,a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,2{}\mathrm{i}+a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+2\,a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,2{}\mathrm{i}}{256\,C^3\,a^{11}\,b-6144\,A^3\,a^4\,b^8+9216\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+1536\,A^3\,a^7\,b^5+64\,A^3\,a^9\,b^3-256\,C^3\,a^6\,b^6-1024\,C^3\,a^8\,b^4+128\,C^3\,a^9\,b^3-1024\,C^3\,a^{10}\,b^2-2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-2\,a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)+2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+2\,a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)+256\,A\,C^2\,a^{11}\,b+64\,A^2\,C\,a^{11}\,b-1536\,A\,C^2\,a^4\,b^8-7296\,A\,C^2\,a^6\,b^6+1536\,A\,C^2\,a^7\,b^5-8704\,A\,C^2\,a^8\,b^4+3456\,A\,C^2\,a^9\,b^3-512\,A\,C^2\,a^{10}\,b^2-6144\,A^2\,C\,a^4\,b^8+4608\,A^2\,C\,a^5\,b^7-13824\,A^2\,C\,a^6\,b^6+13056\,A^2\,C\,a^7\,b^5-1024\,A^2\,C\,a^8\,b^4+1824\,A^2\,C\,a^9\,b^3}\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,4{}\mathrm{i}}{d}","Not used",1,"(a^2*atan(-((a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) - (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2))/2 + (a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) + (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2))/2)/(256*C^3*a^11*b - (a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) - (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2)*1i)/2 + (a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) + (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2)*1i)/2 - 6144*A^3*a^4*b^8 + 9216*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 1536*A^3*a^7*b^5 + 64*A^3*a^9*b^3 - 256*C^3*a^6*b^6 - 1024*C^3*a^8*b^4 + 128*C^3*a^9*b^3 - 1024*C^3*a^10*b^2 + 256*A*C^2*a^11*b + 64*A^2*C*a^11*b - 1536*A*C^2*a^4*b^8 - 7296*A*C^2*a^6*b^6 + 1536*A*C^2*a^7*b^5 - 8704*A*C^2*a^8*b^4 + 3456*A*C^2*a^9*b^3 - 512*A*C^2*a^10*b^2 - 6144*A^2*C*a^4*b^8 + 4608*A^2*C*a^5*b^7 - 13824*A^2*C*a^6*b^6 + 13056*A^2*C*a^7*b^5 - 1024*A^2*C*a^8*b^4 + 1824*A^2*C*a^9*b^3))*(A*a^2 + 12*A*b^2 + 2*C*a^2))/d - (tan(c/2 + (d*x)/2)^5*(6*A*a^4 - 4*A*b^4 + (4*C*b^4)/3 - 24*C*a^2*b^2) - tan(c/2 + (d*x)/2)^3*(4*A*a^4 - (8*C*b^4)/3 + 16*A*a^3*b - 8*C*a*b^3) - tan(c/2 + (d*x)/2)^7*(4*A*a^4 - (8*C*b^4)/3 - 16*A*a^3*b + 8*C*a*b^3) + tan(c/2 + (d*x)/2)*(A*a^4 + 2*A*b^4 + 2*C*b^4 + 12*C*a^2*b^2 + 8*A*a^3*b + 4*C*a*b^3) + tan(c/2 + (d*x)/2)^9*(A*a^4 + 2*A*b^4 + 2*C*b^4 + 12*C*a^2*b^2 - 8*A*a^3*b - 4*C*a*b^3))/(d*(tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - (a*b*atan((a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) - 2*a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b))*(2*A*b^2 + 2*C*a^2 + C*b^2)*2i + a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) + 2*a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b))*(2*A*b^2 + 2*C*a^2 + C*b^2)*2i)/(256*C^3*a^11*b - 6144*A^3*a^4*b^8 + 9216*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 1536*A^3*a^7*b^5 + 64*A^3*a^9*b^3 - 256*C^3*a^6*b^6 - 1024*C^3*a^8*b^4 + 128*C^3*a^9*b^3 - 1024*C^3*a^10*b^2 - 2*a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) - 2*a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b))*(2*A*b^2 + 2*C*a^2 + C*b^2) + 2*a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) + 2*a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b))*(2*A*b^2 + 2*C*a^2 + C*b^2) + 256*A*C^2*a^11*b + 64*A^2*C*a^11*b - 1536*A*C^2*a^4*b^8 - 7296*A*C^2*a^6*b^6 + 1536*A*C^2*a^7*b^5 - 8704*A*C^2*a^8*b^4 + 3456*A*C^2*a^9*b^3 - 512*A*C^2*a^10*b^2 - 6144*A^2*C*a^4*b^8 + 4608*A^2*C*a^5*b^7 - 13824*A^2*C*a^6*b^6 + 13056*A^2*C*a^7*b^5 - 1024*A^2*C*a^8*b^4 + 1824*A^2*C*a^9*b^3))*(2*A*b^2 + 2*C*a^2 + C*b^2)*4i)/d","B"
668,1,2660,251,5.707085,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{\left(2\,A\,a^4+2\,C\,a^4+C\,b^4+12\,A\,a^2\,b^2-4\,A\,a^3\,b-8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{8\,A\,a^4}{3}+8\,A\,a^3\,b-16\,C\,a\,b^3+4\,C\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{4\,A\,a^4}{3}-4\,C\,a^4+6\,C\,b^4-24\,A\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a^4}{3}-8\,A\,a^3\,b+16\,C\,a\,b^3+4\,C\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,C\,a^4+C\,b^4+12\,A\,a^2\,b^2+4\,A\,a^3\,b+8\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)\,1{}\mathrm{i}-\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)+\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2\right)-256\,A^3\,a\,b^{11}+1024\,A^3\,a^2\,b^{10}-128\,A^3\,a^3\,b^9+1024\,A^3\,a^4\,b^8+256\,A^3\,a^6\,b^6-64\,C^3\,a^3\,b^9-1536\,C^3\,a^5\,b^7+512\,C^3\,a^6\,b^6-9216\,C^3\,a^7\,b^5+6144\,C^3\,a^8\,b^4-64\,A\,C^2\,a\,b^{11}-256\,A^2\,C\,a\,b^{11}-1824\,A\,C^2\,a^3\,b^9+1024\,A\,C^2\,a^4\,b^8-13056\,A\,C^2\,a^5\,b^7+13824\,A\,C^2\,a^6\,b^6-4608\,A\,C^2\,a^7\,b^5+6144\,A\,C^2\,a^8\,b^4+512\,A^2\,C\,a^2\,b^{10}-3456\,A^2\,C\,a^3\,b^9+8704\,A^2\,C\,a^4\,b^8-1536\,A^2\,C\,a^5\,b^7+7296\,A^2\,C\,a^6\,b^6+1536\,A^2\,C\,a^8\,b^4}\right)\,\left(A\,b^4\,2{}\mathrm{i}+C\,b^4\,1{}\mathrm{i}+C\,a^2\,b^2\,12{}\mathrm{i}\right)}{d}+\frac{4\,a\,b\,\mathrm{atan}\left(\frac{2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)+2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)}{256\,A^3\,a\,b^{11}-1024\,A^3\,a^2\,b^{10}+128\,A^3\,a^3\,b^9-1024\,A^3\,a^4\,b^8-256\,A^3\,a^6\,b^6+64\,C^3\,a^3\,b^9+1536\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+9216\,C^3\,a^7\,b^5-6144\,C^3\,a^8\,b^4+64\,A\,C^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}+1824\,A\,C^2\,a^3\,b^9-1024\,A\,C^2\,a^4\,b^8+13056\,A\,C^2\,a^5\,b^7-13824\,A\,C^2\,a^6\,b^6+4608\,A\,C^2\,a^7\,b^5-6144\,A\,C^2\,a^8\,b^4-512\,A^2\,C\,a^2\,b^{10}+3456\,A^2\,C\,a^3\,b^9-8704\,A^2\,C\,a^4\,b^8+1536\,A^2\,C\,a^5\,b^7-7296\,A^2\,C\,a^6\,b^6-1536\,A^2\,C\,a^8\,b^4+a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,2{}\mathrm{i}-a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,2{}\mathrm{i}}\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((4*A*a^4)/3 - 4*C*a^4 + 6*C*b^4 - 24*A*a^2*b^2) - tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 - 4*C*b^4 + 8*A*a^3*b - 16*C*a*b^3) - tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 - 4*C*b^4 - 8*A*a^3*b + 16*C*a*b^3) + tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 + 4*A*a^3*b + 8*C*a*b^3) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 - 4*A*a^3*b - 8*C*a*b^3))/(d*(tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (atan((((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2)*1i - ((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2)*1i)/(((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2) + ((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2) - 256*A^3*a*b^11 + 1024*A^3*a^2*b^10 - 128*A^3*a^3*b^9 + 1024*A^3*a^4*b^8 + 256*A^3*a^6*b^6 - 64*C^3*a^3*b^9 - 1536*C^3*a^5*b^7 + 512*C^3*a^6*b^6 - 9216*C^3*a^7*b^5 + 6144*C^3*a^8*b^4 - 64*A*C^2*a*b^11 - 256*A^2*C*a*b^11 - 1824*A*C^2*a^3*b^9 + 1024*A*C^2*a^4*b^8 - 13056*A*C^2*a^5*b^7 + 13824*A*C^2*a^6*b^6 - 4608*A*C^2*a^7*b^5 + 6144*A*C^2*a^8*b^4 + 512*A^2*C*a^2*b^10 - 3456*A^2*C*a^3*b^9 + 8704*A^2*C*a^4*b^8 - 1536*A^2*C*a^5*b^7 + 7296*A^2*C*a^6*b^6 + 1536*A^2*C*a^8*b^4))*(A*b^4*2i + C*b^4*1i + C*a^2*b^2*12i))/d + (4*a*b*atan((2*a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*2i)*(A*a^2 + 2*A*b^2 + 2*C*a^2) + 2*a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*2i)*(A*a^2 + 2*A*b^2 + 2*C*a^2))/(256*A^3*a*b^11 - 1024*A^3*a^2*b^10 + 128*A^3*a^3*b^9 - 1024*A^3*a^4*b^8 - 256*A^3*a^6*b^6 + 64*C^3*a^3*b^9 + 1536*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 9216*C^3*a^7*b^5 - 6144*C^3*a^8*b^4 + a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*2i)*(A*a^2 + 2*A*b^2 + 2*C*a^2)*2i - a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*2i)*(A*a^2 + 2*A*b^2 + 2*C*a^2)*2i + 64*A*C^2*a*b^11 + 256*A^2*C*a*b^11 + 1824*A*C^2*a^3*b^9 - 1024*A*C^2*a^4*b^8 + 13056*A*C^2*a^5*b^7 - 13824*A*C^2*a^6*b^6 + 4608*A*C^2*a^7*b^5 - 6144*A*C^2*a^8*b^4 - 512*A^2*C*a^2*b^10 + 3456*A^2*C*a^3*b^9 - 8704*A^2*C*a^4*b^8 + 1536*A^2*C*a^5*b^7 - 7296*A^2*C*a^6*b^6 - 1536*A^2*C*a^8*b^4))*(A*a^2 + 2*A*b^2 + 2*C*a^2))/d","B"
669,1,395,246,4.394496,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{A\,a^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,b^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{3\,A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{4\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{3\,d}+\frac{C\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{4\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}+\frac{3\,A\,a^2\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}+\frac{4\,A\,a^3\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}-\frac{A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4\,d}-\frac{A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{C\,a\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,8{}\mathrm{i}}{d}-\frac{A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}-\frac{C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,12{}\mathrm{i}}{d}","Not used",1,"(A*a^4*cos(c + d*x)^3*sin(c + d*x))/(4*d) - (A*b^4*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a^4*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d - (C*a*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*8i)/d - (A*a^4*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/(4*d) + (C*b^4*sin(c + d*x))/(d*cos(c + d*x)) - (A*a^2*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/d - (C*a^2*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*12i)/d + (3*A*a^4*cos(c + d*x)*sin(c + d*x))/(8*d) + (4*A*a*b^3*sin(c + d*x))/d + (8*A*a^3*b*sin(c + d*x))/(3*d) + (C*a^4*cos(c + d*x)*sin(c + d*x))/(2*d) + (4*C*a^3*b*sin(c + d*x))/d + (3*A*a^2*b^2*cos(c + d*x)*sin(c + d*x))/d + (4*A*a^3*b*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
670,1,2241,250,5.596611,"\text{Not used}","int(cos(c + d*x)^5*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2-4\,A\,a\,b^3-5\,A\,a^3\,b-4\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^4}{3}+8\,A\,b^4+\frac{16\,C\,a^4}{3}+32\,A\,a^2\,b^2+48\,C\,a^2\,b^2-8\,A\,a\,b^3-2\,A\,a^3\,b-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^4}{15}+12\,A\,b^4+\frac{20\,C\,a^4}{3}+40\,A\,a^2\,b^2+72\,C\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^4}{3}+8\,A\,b^4+\frac{16\,C\,a^4}{3}+32\,A\,a^2\,b^2+48\,C\,a^2\,b^2+8\,A\,a\,b^3+2\,A\,a^3\,b+8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2+4\,A\,a\,b^3+5\,A\,a^3\,b+4\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{C\,b^4\,\mathrm{atan}\left(\frac{C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+C\,b^4\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}+C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-C\,b^4\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}}{1024\,C^3\,a^2\,b^{10}-256\,C^3\,a\,b^{11}-128\,C^3\,a^3\,b^9+1024\,C^3\,a^4\,b^8+256\,C^3\,a^6\,b^6+C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+C\,b^4\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)-C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-C\,b^4\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)-128\,A\,C^2\,a\,b^{11}+1024\,A\,C^2\,a^2\,b^{10}-96\,A\,C^2\,a^3\,b^9+1280\,A\,C^2\,a^4\,b^8+384\,A\,C^2\,a^6\,b^6+256\,A^2\,C\,a^2\,b^{10}+384\,A^2\,C\,a^4\,b^8+144\,A^2\,C\,a^6\,b^6}\right)\,2{}\mathrm{i}}{d}-\frac{a\,b\,\mathrm{atan}\left(\frac{\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-\frac{a\,b\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)}{2}+\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+\frac{a\,b\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)}{2}}{1024\,C^3\,a^2\,b^{10}-256\,C^3\,a\,b^{11}-128\,C^3\,a^3\,b^9+1024\,C^3\,a^4\,b^8+256\,C^3\,a^6\,b^6-128\,A\,C^2\,a\,b^{11}+1024\,A\,C^2\,a^2\,b^{10}-96\,A\,C^2\,a^3\,b^9+1280\,A\,C^2\,a^4\,b^8+384\,A\,C^2\,a^6\,b^6+256\,A^2\,C\,a^2\,b^{10}+384\,A^2\,C\,a^4\,b^8+144\,A^2\,C\,a^6\,b^6-\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-\frac{a\,b\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)\,1{}\mathrm{i}}{2}+\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+\frac{a\,b\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)\,\left(32\,C\,b^4+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)\,1{}\mathrm{i}}{2}}\right)\,\left(3\,A\,a^2+4\,A\,b^2+4\,C\,a^2+8\,C\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 + 4*A*a*b^3 + 5*A*a^3*b + 4*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^4)/15 + 12*A*b^4 + (20*C*a^4)/3 + 40*A*a^2*b^2 + 72*C*a^2*b^2) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 - 4*A*a*b^3 - 5*A*a^3*b - 4*C*a^3*b) + tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 + 8*A*b^4 + (16*C*a^4)/3 + 32*A*a^2*b^2 + 48*C*a^2*b^2 + 8*A*a*b^3 + 2*A*a^3*b + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 + 8*A*b^4 + (16*C*a^4)/3 + 32*A*a^2*b^2 + 48*C*a^2*b^2 - 8*A*a*b^3 - 2*A*a^3*b - 8*C*a^3*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (C*b^4*atan((C*b^4*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) + C*b^4*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*1i + C*b^4*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) - C*b^4*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*1i)/(1024*C^3*a^2*b^10 - 256*C^3*a*b^11 - 128*C^3*a^3*b^9 + 1024*C^3*a^4*b^8 + 256*C^3*a^6*b^6 + C*b^4*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) + C*b^4*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)) - C*b^4*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) - C*b^4*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)) - 128*A*C^2*a*b^11 + 1024*A*C^2*a^2*b^10 - 96*A*C^2*a^3*b^9 + 1280*A*C^2*a^4*b^8 + 384*A*C^2*a^6*b^6 + 256*A^2*C*a^2*b^10 + 384*A^2*C*a^4*b^8 + 144*A^2*C*a^6*b^6))*2i)/d - (a*b*atan(((a*b*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) - (a*b*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2)*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2))/2 + (a*b*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) + (a*b*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2)*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2))/2)/(1024*C^3*a^2*b^10 - 256*C^3*a*b^11 - 128*C^3*a^3*b^9 + 1024*C^3*a^4*b^8 + 256*C^3*a^6*b^6 - 128*A*C^2*a*b^11 + 1024*A*C^2*a^2*b^10 - 96*A*C^2*a^3*b^9 + 1280*A*C^2*a^4*b^8 + 384*A*C^2*a^6*b^6 + 256*A^2*C*a^2*b^10 + 384*A^2*C*a^4*b^8 + 144*A^2*C*a^6*b^6 - (a*b*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) - (a*b*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2)*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2)*1i)/2 + (a*b*(tan(c/2 + (d*x)/2)*(32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2) + (a*b*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2)*(32*C*b^4 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2)*1i)/2))*(3*A*a^2 + 4*A*b^2 + 4*C*a^2 + 8*C*b^2))/d","B"
671,1,359,298,4.339204,"\text{Not used}","int(cos(c + d*x)^6*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{5\,A\,a^4\,x}{16}+\frac{A\,b^4\,x}{2}+\frac{3\,C\,a^4\,x}{8}+C\,b^4\,x+\frac{9\,A\,a^2\,b^2\,x}{4}+3\,C\,a^2\,b^2\,x+\frac{15\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{A\,a^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{5\,A\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{A\,a^3\,b\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{C\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{4\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(5*A*a^4*x)/16 + (A*b^4*x)/2 + (3*C*a^4*x)/8 + C*b^4*x + (9*A*a^2*b^2*x)/4 + 3*C*a^2*b^2*x + (15*A*a^4*sin(2*c + 2*d*x))/(64*d) + (3*A*a^4*sin(4*c + 4*d*x))/(64*d) + (A*a^4*sin(6*c + 6*d*x))/(192*d) + (A*b^4*sin(2*c + 2*d*x))/(4*d) + (C*a^4*sin(2*c + 2*d*x))/(4*d) + (C*a^4*sin(4*c + 4*d*x))/(32*d) + (A*a*b^3*sin(3*c + 3*d*x))/(3*d) + (5*A*a^3*b*sin(3*c + 3*d*x))/(12*d) + (A*a^3*b*sin(5*c + 5*d*x))/(20*d) + (C*a^3*b*sin(3*c + 3*d*x))/(3*d) + (3*A*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*A*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (3*C*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*A*a*b^3*sin(c + d*x))/d + (5*A*a^3*b*sin(c + d*x))/(2*d) + (4*C*a*b^3*sin(c + d*x))/d + (3*C*a^3*b*sin(c + d*x))/d","B"
672,1,751,339,6.801571,"\text{Not used}","int(cos(c + d*x)^7*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^4,x)","\frac{\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2-5\,A\,a\,b^3-\frac{11\,A\,a^3\,b}{2}-4\,C\,a\,b^3-5\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(4\,A\,a^4+\frac{28\,A\,b^4}{3}+\frac{20\,C\,a^4}{3}+12\,C\,b^4+40\,A\,a^2\,b^2+56\,C\,a^2\,b^2-12\,A\,a\,b^3-\frac{14\,A\,a^3\,b}{3}-16\,C\,a\,b^3-12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{86\,A\,a^4}{5}+\frac{58\,A\,b^4}{3}+\frac{226\,C\,a^4}{15}+30\,C\,b^4+\frac{452\,A\,a^2\,b^2}{5}+116\,C\,a^2\,b^2-9\,A\,a\,b^3-\frac{85\,A\,a^3\,b}{6}-20\,C\,a\,b^3-9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{424\,A\,a^4}{35}+24\,A\,b^4+\frac{104\,C\,a^4}{5}+40\,C\,b^4+\frac{624\,A\,a^2\,b^2}{5}+144\,C\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{86\,A\,a^4}{5}+\frac{58\,A\,b^4}{3}+\frac{226\,C\,a^4}{15}+30\,C\,b^4+\frac{452\,A\,a^2\,b^2}{5}+116\,C\,a^2\,b^2+9\,A\,a\,b^3+\frac{85\,A\,a^3\,b}{6}+20\,C\,a\,b^3+9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A\,a^4+\frac{28\,A\,b^4}{3}+\frac{20\,C\,a^4}{3}+12\,C\,b^4+40\,A\,a^2\,b^2+56\,C\,a^2\,b^2+12\,A\,a\,b^3+\frac{14\,A\,a^3\,b}{3}+16\,C\,a\,b^3+12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2+5\,A\,a\,b^3+\frac{11\,A\,a^3\,b}{2}+4\,C\,a\,b^3+5\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^2+6\,A\,b^2+6\,C\,a^2+8\,C\,b^2\right)}{2\,\left(3\,A\,a\,b^3+\frac{5\,A\,a^3\,b}{2}+4\,C\,a\,b^3+3\,C\,a^3\,b\right)}\right)\,\left(5\,A\,a^2+6\,A\,b^2+6\,C\,a^2+8\,C\,b^2\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 + 5*A*a*b^3 + (11*A*a^3*b)/2 + 4*C*a*b^3 + 5*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((424*A*a^4)/35 + 24*A*b^4 + (104*C*a^4)/5 + 40*C*b^4 + (624*A*a^2*b^2)/5 + 144*C*a^2*b^2) + tan(c/2 + (d*x)/2)^13*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 - 5*A*a*b^3 - (11*A*a^3*b)/2 - 4*C*a*b^3 - 5*C*a^3*b) + tan(c/2 + (d*x)/2)^3*(4*A*a^4 + (28*A*b^4)/3 + (20*C*a^4)/3 + 12*C*b^4 + 40*A*a^2*b^2 + 56*C*a^2*b^2 + 12*A*a*b^3 + (14*A*a^3*b)/3 + 16*C*a*b^3 + 12*C*a^3*b) + tan(c/2 + (d*x)/2)^11*(4*A*a^4 + (28*A*b^4)/3 + (20*C*a^4)/3 + 12*C*b^4 + 40*A*a^2*b^2 + 56*C*a^2*b^2 - 12*A*a*b^3 - (14*A*a^3*b)/3 - 16*C*a*b^3 - 12*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((86*A*a^4)/5 + (58*A*b^4)/3 + (226*C*a^4)/15 + 30*C*b^4 + (452*A*a^2*b^2)/5 + 116*C*a^2*b^2 + 9*A*a*b^3 + (85*A*a^3*b)/6 + 20*C*a*b^3 + 9*C*a^3*b) + tan(c/2 + (d*x)/2)^9*((86*A*a^4)/5 + (58*A*b^4)/3 + (226*C*a^4)/15 + 30*C*b^4 + (452*A*a^2*b^2)/5 + 116*C*a^2*b^2 - 9*A*a*b^3 - (85*A*a^3*b)/6 - 20*C*a*b^3 - 9*C*a^3*b))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(5*A*a^2 + 6*A*b^2 + 6*C*a^2 + 8*C*b^2))/(2*(3*A*a*b^3 + (5*A*a^3*b)/2 + 4*C*a*b^3 + 3*C*a^3*b)))*(5*A*a^2 + 6*A*b^2 + 6*C*a^2 + 8*C*b^2))/(2*d)","B"
673,1,274,158,4.070683,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,a^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{3\,b^5\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{b^5\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}-\frac{2\,a\,b^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{a\,b^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^3}+\frac{2\,a^3\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{a^2\,b^3\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{b^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4\,d}+\frac{a^2\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{a^4\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}","Not used",1,"(2*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^5*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/(4*d) - (3*b^5*sin(c + d*x))/(8*d*cos(c + d*x)^2) - (b^5*sin(c + d*x))/(4*d*cos(c + d*x)^4) + (a^2*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (a^4*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/d - (2*a*b^4*sin(c + d*x))/(d*cos(c + d*x)) - (a*b^4*sin(c + d*x))/(d*cos(c + d*x)^3) + (2*a^3*b^2*sin(c + d*x))/(d*cos(c + d*x)) - (a^2*b^3*sin(c + d*x))/(d*cos(c + d*x)^2)","B"
674,1,160,106,3.618030,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{2\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,b^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}-\frac{b^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}-\frac{2\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,b^3\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(2*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*b^4*sin(c + d*x))/(3*d*cos(c + d*x)) - (b^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) - (2*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*b^3*sin(c + d*x))/(d*cos(c + d*x)^2)","B"
675,1,137,75,3.589173,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{2\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{b^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{2\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (b^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (2*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*b^2*sin(c + d*x))/(d*cos(c + d*x))","B"
676,1,3914,186,8.042532,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^2+2\,C\,a^2+2\,C\,b^2+C\,a\,b\right)}{b^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^2+3\,C\,a^2+C\,b^2\right)}{3\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^2+2\,C\,a^2+2\,C\,b^2-C\,a\,b\right)}{b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)\,1{}\mathrm{i}}{b^4}-\frac{\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)\,1{}\mathrm{i}}{b^4}}{\frac{\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)}{b^4}-\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}+\frac{\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)}{b^4}}\right)\,\left(C\,a^3+b^2\,\left(A\,a+\frac{C\,a}{2}\right)\right)\,2{}\mathrm{i}}{b^4\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}-\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"(a^2*atan(((a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 + (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 - (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4))/b^9 - (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 + (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) + (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 - (a^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*2i)/(d*(b^6 - a^2*b^4)) - (atan((((C*a^3 + b^2*(A*a + (C*a)/2))*((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(C*a^3 + b^2*(A*a + (C*a)/2))*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3 + b^2*(A*a + (C*a)/2)))/b^4 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6)*1i)/b^4 - ((C*a^3 + b^2*(A*a + (C*a)/2))*((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(C*a^3 + b^2*(A*a + (C*a)/2))*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3 + b^2*(A*a + (C*a)/2)))/b^4 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6)*1i)/b^4)/(((C*a^3 + b^2*(A*a + (C*a)/2))*((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(C*a^3 + b^2*(A*a + (C*a)/2))*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3 + b^2*(A*a + (C*a)/2)))/b^4 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6))/b^4 - (16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4))/b^9 + ((C*a^3 + b^2*(A*a + (C*a)/2))*((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(C*a^3 + b^2*(A*a + (C*a)/2))*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3 + b^2*(A*a + (C*a)/2)))/b^4 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6))/b^4))*(C*a^3 + b^2*(A*a + (C*a)/2))*2i)/(b^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*A*b^2 + 2*C*a^2 + 2*C*b^2 + C*a*b))/b^3 - (4*tan(c/2 + (d*x)/2)^3*(3*A*b^2 + 3*C*a^2 + C*b^2))/(3*b^3) + (tan(c/2 + (d*x)/2)*(2*A*b^2 + 2*C*a^2 + 2*C*b^2 - C*a*b))/b^3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
677,1,2321,137,6.876813,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a-C\,b\right)}{b^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a+C\,b\right)}{b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{a^2-b^2}\right)\,\left(C\,a^3\,\sqrt{a^2-b^2}+A\,a\,b^2\,\sqrt{a^2-b^2}\right)}{b^3\,d\,\left(a^2-b^2\right)}-\frac{a\,\ln\left(\frac{8\,a\,\left(a-b\right)\,\left(4\,A^3\,b^6+12\,A^2\,C\,a^2\,b^4-2\,A^2\,C\,a\,b^5+4\,A^2\,C\,b^6+12\,A\,C^2\,a^4\,b^2-4\,A\,C^2\,a^3\,b^3+8\,A\,C^2\,a^2\,b^4-A\,C^2\,a\,b^5+A\,C^2\,b^6+4\,C^3\,a^6-2\,C^3\,a^5\,b+4\,C^3\,a^4\,b^2-C^3\,a^3\,b^3+C^3\,a^2\,b^4\right)}{b^6}-\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-b\right)\,\left(8\,A^2\,a^2\,b^4-8\,A^2\,a\,b^5+4\,A^2\,b^6+16\,A\,C\,a^4\,b^2-16\,A\,C\,a^3\,b^3+12\,A\,C\,a^2\,b^4-8\,A\,C\,a\,b^5+4\,A\,C\,b^6+8\,C^2\,a^6-8\,C^2\,a^5\,b+8\,C^2\,a^4\,b^2-8\,C^2\,a^3\,b^3+5\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{b^4}+\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(16\,{\left(a-b\right)}^2\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2+C\,a\,b\right)-\frac{64\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,{\left(a-b\right)}^2}{b^5-a^2\,b^3}\right)\,\left(C\,a^2+A\,b^2\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)}{d\,\left(b^5-a^2\,b^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(4\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+12\,A^2\,C\,a^4\,b^4-14\,A^2\,C\,a^3\,b^5+6\,A^2\,C\,a^2\,b^6-4\,A^2\,C\,a\,b^7+12\,A\,C^2\,a^6\,b^2-16\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4-9\,A\,C^2\,a^3\,b^5+2\,A\,C^2\,a^2\,b^6-A\,C^2\,a\,b^7+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}-\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)}{b^3}+\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)}{b^3}}\right)\,\left(C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^3\,d}","Not used",1,"(atan((((C*a^2 + b^2*(A + C/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 + ((C*a^2 + b^2*(A + C/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3)*1i)/b^3 + ((C*a^2 + b^2*(A + C/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 - ((C*a^2 + b^2*(A + C/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3)*1i)/b^3)/((16*(4*C^3*a^8 - 4*A^3*a*b^7 - 6*C^3*a^7*b + 4*A^3*a^2*b^6 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - A*C^2*a*b^7 - 4*A^2*C*a*b^7 + 2*A*C^2*a^2*b^6 - 9*A*C^2*a^3*b^5 + 12*A*C^2*a^4*b^4 - 16*A*C^2*a^5*b^3 + 12*A*C^2*a^6*b^2 + 6*A^2*C*a^2*b^6 - 14*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4))/b^6 - ((C*a^2 + b^2*(A + C/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 + ((C*a^2 + b^2*(A + C/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3))/b^3 + ((C*a^2 + b^2*(A + C/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 - ((C*a^2 + b^2*(A + C/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3))/b^3))*(C*a^2 + b^2*(A + C/2))*2i)/(b^3*d) - ((tan(c/2 + (d*x)/2)*(2*C*a - C*b))/b^2 - (tan(c/2 + (d*x)/2)^3*(2*C*a + C*b))/b^2)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) - (log(a*tan(c/2 + (d*x)/2) - b*tan(c/2 + (d*x)/2) + (a^2 - b^2)^(1/2))*(C*a^3*(a^2 - b^2)^(1/2) + A*a*b^2*(a^2 - b^2)^(1/2)))/(b^3*d*(a^2 - b^2)) - (a*log((8*a*(a - b)*(4*A^3*b^6 + 4*C^3*a^6 + A*C^2*b^6 + 4*A^2*C*b^6 - 2*C^3*a^5*b + C^3*a^2*b^4 - C^3*a^3*b^3 + 4*C^3*a^4*b^2 - A*C^2*a*b^5 - 2*A^2*C*a*b^5 + 8*A*C^2*a^2*b^4 - 4*A*C^2*a^3*b^3 + 12*A*C^2*a^4*b^2 + 12*A^2*C*a^2*b^4))/b^6 - (a*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(a - b)*(4*A^2*b^6 + 8*C^2*a^6 + C^2*b^6 - 8*A^2*a*b^5 - 2*C^2*a*b^5 - 8*C^2*a^5*b + 8*A^2*a^2*b^4 + 5*C^2*a^2*b^4 - 8*C^2*a^3*b^3 + 8*C^2*a^4*b^2 + 4*A*C*b^6 - 8*A*C*a*b^5 + 12*A*C*a^2*b^4 - 16*A*C*a^3*b^3 + 16*A*C*a^4*b^2))/b^4 + (a*((a + b)*(a - b))^(1/2)*(16*(a - b)^2*(2*A*b^2 + 2*C*a^2 + C*b^2 + C*a*b) - (64*a^2*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(a - b)^2)/(b^5 - a^2*b^3))*(A*b^2 + C*a^2))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2))/(d*(b^5 - a^2*b^3))","B"
678,1,934,95,6.063734,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))),x)","-\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{64\,C^3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,C^3\,a^3+128\,A\,C^2\,a^3-\frac{64\,C^3\,a^4}{b}+64\,A^2\,C\,a\,b^2-64\,A^2\,C\,a^2\,b-\frac{128\,A\,C^2\,a^4}{b}}+\frac{64\,C^3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2\,b^2-64\,A^2\,C\,a\,b^3+128\,A\,C^2\,a^4-128\,A\,C^2\,a^3\,b+64\,C^3\,a^4-64\,C^3\,a^3\,b}+\frac{128\,A\,C^2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2\,b^2-64\,A^2\,C\,a\,b^3+128\,A\,C^2\,a^4-128\,A\,C^2\,a^3\,b+64\,C^3\,a^4-64\,C^3\,a^3\,b}+\frac{64\,A^2\,C\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2-\frac{64\,C^3\,a^3}{b}+\frac{64\,C^3\,a^4}{b^2}-64\,A^2\,C\,a\,b-\frac{128\,A\,C^2\,a^3}{b}+\frac{128\,A\,C^2\,a^4}{b^2}}+\frac{128\,A\,C^2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,C^3\,a^3+128\,A\,C^2\,a^3-\frac{64\,C^3\,a^4}{b}+64\,A^2\,C\,a\,b^2-64\,A^2\,C\,a^2\,b-\frac{128\,A\,C^2\,a^4}{b}}-\frac{64\,A^2\,C\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2-\frac{64\,C^3\,a^3}{b}+\frac{64\,C^3\,a^4}{b^2}-64\,A^2\,C\,a\,b-\frac{128\,A\,C^2\,a^3}{b}+\frac{128\,A\,C^2\,a^4}{b^2}}\right)}{b^2\,d}-\frac{\ln\left(b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{a^2-b^2}\right)\,\left(A\,b^2\,\sqrt{a^2-b^2}+C\,a^2\,\sqrt{a^2-b^2}\right)}{b^2\,d\,\left(a^2-b^2\right)}-\frac{\ln\left(\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^4+2\,A\,C\,a^2\,b^2+2\,C^2\,a^4-2\,C^2\,a^3\,b+C^2\,a^2\,b^2\right)}{b^2}+\frac{32\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(a-b\right)\,\left(A\,a^2\,b^2-A\,b^4+C\,a\,b^3-C\,a^3\,b+2\,C\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,A\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)}{\left(b^4-a^2\,b^2\right)\,\left(a+b\right)}\right)}{b^4-a^2\,b^2}+\frac{32\,C\,a\,\left(a-b\right)\,\left(A^2\,b^3+A\,C\,a^2\,b+A\,C\,a\,b^2+C^2\,a^3\right)}{b^3}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)}{d\,\left(b^4-a^2\,b^2\right)}-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- (2*C*a*atanh((64*C^3*a^3*tan(c/2 + (d*x)/2))/(64*C^3*a^3 + 128*A*C^2*a^3 - (64*C^3*a^4)/b + 64*A^2*C*a*b^2 - 64*A^2*C*a^2*b - (128*A*C^2*a^4)/b) + (64*C^3*a^4*tan(c/2 + (d*x)/2))/(64*C^3*a^4 + 128*A*C^2*a^4 - 64*C^3*a^3*b - 128*A*C^2*a^3*b - 64*A^2*C*a*b^3 + 64*A^2*C*a^2*b^2) + (128*A*C^2*a^4*tan(c/2 + (d*x)/2))/(64*C^3*a^4 + 128*A*C^2*a^4 - 64*C^3*a^3*b - 128*A*C^2*a^3*b - 64*A^2*C*a*b^3 + 64*A^2*C*a^2*b^2) + (64*A^2*C*a^2*tan(c/2 + (d*x)/2))/(64*A^2*C*a^2 - (64*C^3*a^3)/b + (64*C^3*a^4)/b^2 - 64*A^2*C*a*b - (128*A*C^2*a^3)/b + (128*A*C^2*a^4)/b^2) + (128*A*C^2*a^3*tan(c/2 + (d*x)/2))/(64*C^3*a^3 + 128*A*C^2*a^3 - (64*C^3*a^4)/b + 64*A^2*C*a*b^2 - 64*A^2*C*a^2*b - (128*A*C^2*a^4)/b) - (64*A^2*C*a*b*tan(c/2 + (d*x)/2))/(64*A^2*C*a^2 - (64*C^3*a^3)/b + (64*C^3*a^4)/b^2 - 64*A^2*C*a*b - (128*A*C^2*a^3)/b + (128*A*C^2*a^4)/b^2)))/(b^2*d) - (log(b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2) + (a^2 - b^2)^(1/2))*(A*b^2*(a^2 - b^2)^(1/2) + C*a^2*(a^2 - b^2)^(1/2)))/(b^2*d*(a^2 - b^2)) - (log((((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((32*tan(c/2 + (d*x)/2)*(a - b)*(A^2*b^4 + 2*C^2*a^4 - 2*C^2*a^3*b + C^2*a^2*b^2 + 2*A*C*a^2*b^2))/b^2 + (32*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(a - b)*(A*a^2*b^2 - A*b^4 + C*a*b^3 - C*a^3*b + 2*C*a^3*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*A*a*b^2*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)))/((b^4 - a^2*b^2)*(a + b))))/(b^4 - a^2*b^2) + (32*C*a*(a - b)*(A^2*b^3 + C^2*a^3 + A*C*a*b^2 + A*C*a^2*b))/b^3)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2))/(d*(b^4 - a^2*b^2)) - (2*C*tan(c/2 + (d*x)/2))/(b*d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
679,1,3656,88,9.805939,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x)),x)","\frac{2\,A\,\mathrm{atan}\left(\frac{16384\,A^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{16384\,A^5\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-16384\,A^5\,a\,b^4+16384\,A^5\,b^5-32768\,A^4\,C\,a\,b^4+32768\,A^4\,C\,b^5-32768\,A^3\,C^2\,a^3\,b^2+32768\,A^3\,C^2\,a^2\,b^3-32768\,A^2\,C^3\,a^3\,b^2+32768\,A^2\,C^3\,a^2\,b^3-16384\,A\,C^4\,a^5+16384\,A\,C^4\,a^4\,b}+\frac{16384\,A\,C^4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^4\,C\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^4\,C\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-16384\,A^5\,a\,b^4+16384\,A^5\,b^5-32768\,A^4\,C\,a\,b^4+32768\,A^4\,C\,b^5-32768\,A^3\,C^2\,a^3\,b^2+32768\,A^3\,C^2\,a^2\,b^3-32768\,A^2\,C^3\,a^3\,b^2+32768\,A^2\,C^3\,a^2\,b^3-16384\,A\,C^4\,a^5+16384\,A\,C^4\,a^4\,b}-\frac{16384\,A\,C^4\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}-\frac{32768\,A^2\,C^3\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}-\frac{32768\,A^3\,C^2\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^2\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^3\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}\right)}{a\,d}+\frac{2\,C\,\mathrm{atanh}\left(\frac{16384\,C^5\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{16384\,C^5\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^4\,C\,a\,b^4-16384\,A^4\,C\,b^5+32768\,A^3\,C^2\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^2\,C^3\,a^2\,b^3+32768\,A\,C^4\,a^5-32768\,A\,C^4\,a^4\,b+16384\,C^5\,a^5-16384\,C^5\,a^4\,b}+\frac{32768\,A\,C^4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{32768\,A\,C^4\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^4\,C\,a\,b^4-16384\,A^4\,C\,b^5+32768\,A^3\,C^2\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^2\,C^3\,a^2\,b^3+32768\,A\,C^4\,a^5-32768\,A\,C^4\,a^4\,b+16384\,C^5\,a^5-16384\,C^5\,a^4\,b}+\frac{16384\,A^4\,C\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}-\frac{16384\,A^4\,C\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}-\frac{32768\,A^2\,C^3\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}-\frac{32768\,A^3\,C^2\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{32768\,A^2\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{32768\,A^3\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}\right)}{b\,d}-\frac{\ln\left(24576\,A^2\,C^3\,a^4-8192\,A^4\,C\,b^4-8192\,A\,C^4\,a^4+24576\,A^3\,C^2\,b^4+16384\,A^2\,C^3\,a^2\,b^2+16384\,A^3\,C^2\,a^2\,b^2+8192\,A\,C^4\,a^3\,b+8192\,A^4\,C\,a\,b^3+8192\,A^2\,C^3\,a\,b^3-49152\,A^2\,C^3\,a^3\,b-49152\,A^3\,C^2\,a\,b^3+8192\,A^3\,C^2\,a^3\,b+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-b\right)\,\left(A^4\,b^4+2\,A^3\,C\,a^2\,b^2+2\,A^2\,C^2\,a^4-4\,A^2\,C^2\,a^3\,b+6\,A^2\,C^2\,a^2\,b^2-4\,A^2\,C^2\,a\,b^3+2\,A^2\,C^2\,b^4+2\,A\,C^3\,a^2\,b^2+C^4\,a^4\right)+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(24576\,C^3\,a^6-24576\,A^3\,b^6+49152\,A^3\,a\,b^5-49152\,C^3\,a^5\,b-32768\,A^3\,a^2\,b^4+8192\,A^3\,a^3\,b^3-8192\,C^3\,a^3\,b^3+32768\,C^3\,a^4\,b^2+8192\,A\,C^2\,a^5\,b-8192\,A^2\,C\,a\,b^5+24576\,A\,C^2\,a^2\,b^4-65536\,A\,C^2\,a^3\,b^3+32768\,A\,C^2\,a^4\,b^2-32768\,A^2\,C\,a^2\,b^4+65536\,A^2\,C\,a^3\,b^3-24576\,A^2\,C\,a^4\,b^2+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(16384\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a-b\right)}^2\,\left(-A^2\,a^3\,b^2+A^2\,a^2\,b^3-A^2\,a\,b^4+A^2\,b^5+A\,C\,a^3\,b^2+A\,C\,a^2\,b^3+C^2\,a^5-C^2\,a^4\,b+C^2\,a^3\,b^2-C^2\,a^2\,b^3\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2+\frac{16384\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,{\left(a-b\right)}^3\,\left(a^2+b^2\right)}{a^2-b^2}\right)}{a\,b\,\left(a^2-b^2\right)}\right)}{a\,b\,\left(a^2-b^2\right)}\right)}{a\,b\,\left(a^2-b^2\right)}\right)}{a\,b\,\left(a^2-b^2\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)}{d\,\left(a\,b^3-a^3\,b\right)}-\frac{\ln\left(a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{a^2-b^2}\right)\,\left(A\,b^2\,\sqrt{a^2-b^2}+C\,a^2\,\sqrt{a^2-b^2}\right)}{a\,b\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*A*atan((16384*A^5*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (16384*A^5*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4) + (16384*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^4*C*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4) - (16384*A*C^4*a^3*b*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) - (32768*A^2*C^3*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) - (32768*A^3*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a)))/(a*d) + (2*C*atanh((16384*C^5*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (16384*C^5*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4) + (32768*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (32768*A*C^4*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4) + (16384*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) - (16384*A^4*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) - (32768*A^2*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) - (32768*A^3*C^2*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b)))/(b*d) - (log(24576*A^2*C^3*a^4 - 8192*A^4*C*b^4 - 8192*A*C^4*a^4 + 24576*A^3*C^2*b^4 + 16384*A^2*C^3*a^2*b^2 + 16384*A^3*C^2*a^2*b^2 + 8192*A*C^4*a^3*b + 8192*A^4*C*a*b^3 + 8192*A^2*C^3*a*b^3 - 49152*A^2*C^3*a^3*b - 49152*A^3*C^2*a*b^3 + 8192*A^3*C^2*a^3*b + (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8192*tan(c/2 + (d*x)/2)*(a - b)*(A^4*b^4 + C^4*a^4 + 2*A^2*C^2*a^4 + 2*A^2*C^2*b^4 + 6*A^2*C^2*a^2*b^2 + 2*A*C^3*a^2*b^2 - 4*A^2*C^2*a*b^3 - 4*A^2*C^2*a^3*b + 2*A^3*C*a^2*b^2) + (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(24576*C^3*a^6 - 24576*A^3*b^6 + 49152*A^3*a*b^5 - 49152*C^3*a^5*b - 32768*A^3*a^2*b^4 + 8192*A^3*a^3*b^3 - 8192*C^3*a^3*b^3 + 32768*C^3*a^4*b^2 + 8192*A*C^2*a^5*b - 8192*A^2*C*a*b^5 + 24576*A*C^2*a^2*b^4 - 65536*A*C^2*a^3*b^3 + 32768*A*C^2*a^4*b^2 - 32768*A^2*C*a^2*b^4 + 65536*A^2*C*a^3*b^3 - 24576*A^2*C*a^4*b^2 + (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(16384*tan(c/2 + (d*x)/2)*(a - b)^2*(A^2*b^5 + C^2*a^5 - A^2*a*b^4 - C^2*a^4*b + A^2*a^2*b^3 - A^2*a^3*b^2 - C^2*a^2*b^3 + C^2*a^3*b^2 + A*C*a^2*b^3 + A*C*a^3*b^2) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 + (16384*a*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(a - b)^3*(a^2 + b^2))/(a^2 - b^2)))/(a*b*(a^2 - b^2))))/(a*b*(a^2 - b^2))))/(a*b*(a^2 - b^2))))/(a*b*(a^2 - b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2))/(d*(a*b^3 - a^3*b)) - (log(a*tan(c/2 + (d*x)/2) - b*tan(c/2 + (d*x)/2) + (a^2 - b^2)^(1/2))*(A*b^2*(a^2 - b^2)^(1/2) + C*a^2*(a^2 - b^2)^(1/2)))/(a*b*d*(a^2 - b^2))","B"
680,1,1560,86,4.338051,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{2\,A\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{A\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{2\,A\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{A\,b^2\,\mathrm{atan}\left(\frac{A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}-C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}+A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}-C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}+A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}","Not used",1,"(2*A*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) + (A*a^3*sin(c + d*x))/(d*(a^4 - a^2*b^2)) - (A*a*b^2*sin(c + d*x))/(d*(a^4 - a^2*b^2)) - (2*A*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) + (A*b^2*atan((A^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - C^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i + A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i)/(C^2*a^8*cos(c/2 + (d*x)/2) + A^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*A^2*a^4*b^4*cos(c/2 + (d*x)/2) + A^2*a^6*b^2*cos(c/2 + (d*x)/2) + C^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*C^2*a^6*b^2*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2)) + (C*a^2*atan((A^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - C^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i + A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i)/(C^2*a^8*cos(c/2 + (d*x)/2) + A^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*A^2*a^4*b^4*cos(c/2 + (d*x)/2) + A^2*a^6*b^2*cos(c/2 + (d*x)/2) + C^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*C^2*a^6*b^2*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2))","B"
681,1,2478,128,6.215547,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d\,\left(a^2-b^2\right)}+\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^5+3\,A^2\,a^3\,b^2+4\,A\,C\,a^5+4\,A\,C\,a^3\,b^2+4\,C^2\,a^5\right)}\right)}{d\,\left(a^2-b^2\right)}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^5+3\,A^2\,a^3\,b^2+4\,A\,C\,a^5+4\,A\,C\,a^3\,b^2+4\,C^2\,a^5\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{A\,b\,\sin\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}-\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d\,\left(a^2-b^2\right)}+\frac{A\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^5+3\,A^2\,a^3\,b^2+4\,A\,C\,a^5+4\,A\,C\,a^3\,b^2+4\,C^2\,a^5\right)}\right)}{a\,d\,\left(a^2-b^2\right)}-\frac{2\,A\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^5+3\,A^2\,a^3\,b^2+4\,A\,C\,a^5+4\,A\,C\,a^3\,b^2+4\,C^2\,a^5\right)}\right)}{a^3\,d\,\left(a^2-b^2\right)}-\frac{2\,C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^5+3\,A^2\,a^3\,b^2+4\,A\,C\,a^5+4\,A\,C\,a^3\,b^2+4\,C^2\,a^5\right)}\right)}{a\,d\,\left(a^2-b^2\right)}+\frac{A\,b^3\,\sin\left(c+d\,x\right)}{a^2\,d\,\left(a^2-b^2\right)}+\frac{C\,b\,\mathrm{atan}\left(\frac{\left(8\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-A^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,A^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A\,C\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+A^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,C^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,A^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+8\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-12\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+16\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,A\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,A\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4+4\,A\,C\,a^7-4\,A\,C\,a^3\,b^4+4\,C^2\,a^7-4\,C^2\,a^5\,b^2\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,2{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)}+\frac{A\,b^3\,\mathrm{atan}\left(\frac{\left(8\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-A^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,A^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A\,C\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+A^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,C^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,A^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+8\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-12\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+16\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,A\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,A\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4+4\,A\,C\,a^7-4\,A\,C\,a^3\,b^4+4\,C^2\,a^7-4\,C^2\,a^5\,b^2\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,2{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)}","Not used",1,"(A*a*sin(2*c + 2*d*x))/(4*d*(a^2 - b^2)) + (A*a*atan((A^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*a^6*sin(c/2 + (d*x)/2) + 3*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 4*A*C*a^6*sin(c/2 + (d*x)/2) + 4*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(A^2*a^5 + 4*C^2*a^5 + 3*A^2*a^3*b^2 + 4*A*C*a^5 + 4*A*C*a^3*b^2))))/(d*(a^2 - b^2)) + (2*C*a*atan((A^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*a^6*sin(c/2 + (d*x)/2) + 3*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 4*A*C*a^6*sin(c/2 + (d*x)/2) + 4*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(A^2*a^5 + 4*C^2*a^5 + 3*A^2*a^3*b^2 + 4*A*C*a^5 + 4*A*C*a^3*b^2))))/(d*(a^2 - b^2)) - (A*b*sin(c + d*x))/(d*(a^2 - b^2)) - (A*b^2*sin(2*c + 2*d*x))/(4*a*d*(a^2 - b^2)) + (A*b^2*atan((A^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*a^6*sin(c/2 + (d*x)/2) + 3*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 4*A*C*a^6*sin(c/2 + (d*x)/2) + 4*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(A^2*a^5 + 4*C^2*a^5 + 3*A^2*a^3*b^2 + 4*A*C*a^5 + 4*A*C*a^3*b^2))))/(a*d*(a^2 - b^2)) - (2*A*b^4*atan((A^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*a^6*sin(c/2 + (d*x)/2) + 3*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 4*A*C*a^6*sin(c/2 + (d*x)/2) + 4*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(A^2*a^5 + 4*C^2*a^5 + 3*A^2*a^3*b^2 + 4*A*C*a^5 + 4*A*C*a^3*b^2))))/(a^3*d*(a^2 - b^2)) - (2*C*b^2*atan((A^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*a^6*sin(c/2 + (d*x)/2) + 3*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 4*A*C*a^6*sin(c/2 + (d*x)/2) + 4*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(A^2*a^5 + 4*C^2*a^5 + 3*A^2*a^3*b^2 + 4*A*C*a^5 + 4*A*C*a^3*b^2))))/(a*d*(a^2 - b^2)) + (A*b^3*sin(c + d*x))/(a^2*d*(a^2 - b^2)) + (C*b*atan(((8*A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - A^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*A^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*C^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A*C*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + A^2*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*C^2*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*A^2*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 8*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 12*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*C*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 16*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*A*C*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*A*C*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*C*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(A^2*a^7 + 4*C^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*C^2*a^5*b^2 + 4*A*C*a^7 - 4*A*C*a^3*b^4)))*((a + b)*(a - b))^(1/2)*2i)/(a*d*(a^2 - b^2)) + (A*b^3*atan(((8*A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - A^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*A^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*C^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A*C*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + A^2*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*C^2*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*A^2*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 8*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 12*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*C*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 16*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*A*C*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*A*C*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*C*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(A^2*a^7 + 4*C^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*C^2*a^5*b^2 + 4*A*C*a^7 - 4*A*C*a^3*b^4)))*((a + b)*(a - b))^(1/2)*2i)/(a^3*d*(a^2 - b^2))","B"
682,1,3942,175,7.607464,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+A\,a\,b\right)}{a^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^2+3\,A\,b^2+3\,C\,a^2\right)}{3\,a^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2-A\,a\,b\right)}{a^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)}{a^4}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)}{a^4}}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + A*a*b))/a^3 + (4*tan(c/2 + (d*x)/2)^3*(A*a^2 + 3*A*b^2 + 3*C*a^2))/(3*a^3) + (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 - A*a*b))/a^3)/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) - (atan(((((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 + (((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2))/a^4)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*1i)/a^4 + (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 - (((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2))/a^4)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*1i)/a^4)/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4))/a^9 + (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 + (((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2))/a^4)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2))/a^4 - (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 - (((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2))/a^4)*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2))/a^4))*(A*b^3*1i + (a^2*b*(A + 2*C)*1i)/2)*2i)/(a^4*d) - (b^2*atan(((b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 + (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 - (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4))/a^9 + (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 + (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) - (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 - (b^2*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*2i)/(d*(a^6 - a^4*b^2))","B"
683,1,5828,232,10.297410,"\text{Not used}","int((cos(c + d*x)^4*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,A\,a^3+8\,A\,b^3+4\,C\,a^3+4\,A\,a\,b^2+8\,A\,a^2\,b+8\,C\,a^2\,b\right)}{4\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,A\,a^3+72\,A\,b^3-12\,C\,a^3-12\,A\,a\,b^2+40\,A\,a^2\,b+72\,C\,a^2\,b\right)}{12\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,A\,b^3-9\,A\,a^3+12\,C\,a^3+12\,A\,a\,b^2+40\,A\,a^2\,b+72\,C\,a^2\,b\right)}{12\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^3-8\,A\,b^3+4\,C\,a^3+4\,A\,a\,b^2-8\,A\,a^2\,b-8\,C\,a^2\,b\right)}{4\,a^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{a^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{a^5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)\,1{}\mathrm{i}}{a^5}}{\frac{-9\,A^3\,a^9\,b^5+18\,A^3\,a^8\,b^6-33\,A^3\,a^7\,b^7+48\,A^3\,a^6\,b^8-88\,A^3\,a^5\,b^9+104\,A^3\,a^4\,b^{10}-104\,A^3\,a^3\,b^{11}+96\,A^3\,a^2\,b^{12}-96\,A^3\,a\,b^{13}+64\,A^3\,b^{14}-9\,A^2\,C\,a^{11}\,b^3+18\,A^2\,C\,a^{10}\,b^4-57\,A^2\,C\,a^9\,b^5+96\,A^2\,C\,a^8\,b^6-192\,A^2\,C\,a^7\,b^7+240\,A^2\,C\,a^6\,b^8-288\,A^2\,C\,a^5\,b^9+288\,A^2\,C\,a^4\,b^{10}-288\,A^2\,C\,a^3\,b^{11}+192\,A^2\,C\,a^2\,b^{12}-24\,A\,C^2\,a^{11}\,b^3+48\,A\,C^2\,a^{10}\,b^4-120\,A\,C^2\,a^9\,b^5+168\,A\,C^2\,a^8\,b^6-264\,A\,C^2\,a^7\,b^7+288\,A\,C^2\,a^6\,b^8-288\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}-16\,C^3\,a^{11}\,b^3+32\,C^3\,a^{10}\,b^4-80\,C^3\,a^9\,b^5+96\,C^3\,a^8\,b^6-96\,C^3\,a^7\,b^7+64\,C^3\,a^6\,b^8}{a^{12}}+\frac{\left(\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{a^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{a^5}+\frac{\left(\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{a^5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)}{a^5}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{-9\,A^3\,a^9\,b^5+18\,A^3\,a^8\,b^6-33\,A^3\,a^7\,b^7+48\,A^3\,a^6\,b^8-88\,A^3\,a^5\,b^9+104\,A^3\,a^4\,b^{10}-104\,A^3\,a^3\,b^{11}+96\,A^3\,a^2\,b^{12}-96\,A^3\,a\,b^{13}+64\,A^3\,b^{14}-9\,A^2\,C\,a^{11}\,b^3+18\,A^2\,C\,a^{10}\,b^4-57\,A^2\,C\,a^9\,b^5+96\,A^2\,C\,a^8\,b^6-192\,A^2\,C\,a^7\,b^7+240\,A^2\,C\,a^6\,b^8-288\,A^2\,C\,a^5\,b^9+288\,A^2\,C\,a^4\,b^{10}-288\,A^2\,C\,a^3\,b^{11}+192\,A^2\,C\,a^2\,b^{12}-24\,A\,C^2\,a^{11}\,b^3+48\,A\,C^2\,a^{10}\,b^4-120\,A\,C^2\,a^9\,b^5+168\,A\,C^2\,a^8\,b^6-264\,A\,C^2\,a^7\,b^7+288\,A\,C^2\,a^6\,b^8-288\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}-16\,C^3\,a^{11}\,b^3+32\,C^3\,a^{10}\,b^4-80\,C^3\,a^9\,b^5+96\,C^3\,a^8\,b^6-96\,C^3\,a^7\,b^7+64\,C^3\,a^6\,b^8}{a^{12}}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^7*(5*A*a^3 + 8*A*b^3 + 4*C*a^3 + 4*A*a*b^2 + 8*A*a^2*b + 8*C*a^2*b))/(4*a^4) + (tan(c/2 + (d*x)/2)^3*(9*A*a^3 + 72*A*b^3 - 12*C*a^3 - 12*A*a*b^2 + 40*A*a^2*b + 72*C*a^2*b))/(12*a^4) + (tan(c/2 + (d*x)/2)^5*(72*A*b^3 - 9*A*a^3 + 12*C*a^3 + 12*A*a*b^2 + 40*A*a^2*b + 72*C*a^2*b))/(12*a^4) - (tan(c/2 + (d*x)/2)*(5*A*a^3 - 8*A*b^3 + 4*C*a^3 + 4*A*a*b^2 - 8*A*a^2*b - 8*C*a^2*b))/(4*a^4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atan(((((((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 - (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/a^5 + (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2))*1i)/a^5 - (((((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 + (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/a^5 - (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2))*1i)/a^5)/((64*A^3*b^14 - 96*A^3*a*b^13 + 96*A^3*a^2*b^12 - 104*A^3*a^3*b^11 + 104*A^3*a^4*b^10 - 88*A^3*a^5*b^9 + 48*A^3*a^6*b^8 - 33*A^3*a^7*b^7 + 18*A^3*a^8*b^6 - 9*A^3*a^9*b^5 + 64*C^3*a^6*b^8 - 96*C^3*a^7*b^7 + 96*C^3*a^8*b^6 - 80*C^3*a^9*b^5 + 32*C^3*a^10*b^4 - 16*C^3*a^11*b^3 + 192*A*C^2*a^4*b^10 - 288*A*C^2*a^5*b^9 + 288*A*C^2*a^6*b^8 - 264*A*C^2*a^7*b^7 + 168*A*C^2*a^8*b^6 - 120*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 - 24*A*C^2*a^11*b^3 + 192*A^2*C*a^2*b^12 - 288*A^2*C*a^3*b^11 + 288*A^2*C*a^4*b^10 - 288*A^2*C*a^5*b^9 + 240*A^2*C*a^6*b^8 - 192*A^2*C*a^7*b^7 + 96*A^2*C*a^8*b^6 - 57*A^2*C*a^9*b^5 + 18*A^2*C*a^10*b^4 - 9*A^2*C*a^11*b^3)/a^12 + (((((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 - (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/a^5 + (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/a^5 + (((((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 + (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/a^5 - (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2)))/a^5))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2))*2i)/(a^5*d) - (b^3*atan(((b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8) + (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 - (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2) + (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8) - (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 + (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2))/((64*A^3*b^14 - 96*A^3*a*b^13 + 96*A^3*a^2*b^12 - 104*A^3*a^3*b^11 + 104*A^3*a^4*b^10 - 88*A^3*a^5*b^9 + 48*A^3*a^6*b^8 - 33*A^3*a^7*b^7 + 18*A^3*a^8*b^6 - 9*A^3*a^9*b^5 + 64*C^3*a^6*b^8 - 96*C^3*a^7*b^7 + 96*C^3*a^8*b^6 - 80*C^3*a^9*b^5 + 32*C^3*a^10*b^4 - 16*C^3*a^11*b^3 + 192*A*C^2*a^4*b^10 - 288*A*C^2*a^5*b^9 + 288*A*C^2*a^6*b^8 - 264*A*C^2*a^7*b^7 + 168*A*C^2*a^8*b^6 - 120*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 - 24*A*C^2*a^11*b^3 + 192*A^2*C*a^2*b^12 - 288*A^2*C*a^3*b^11 + 288*A^2*C*a^4*b^10 - 288*A^2*C*a^5*b^9 + 240*A^2*C*a^6*b^8 - 192*A^2*C*a^7*b^7 + 96*A^2*C*a^8*b^6 - 57*A^2*C*a^9*b^5 + 18*A^2*C*a^10*b^4 - 9*A^2*C*a^11*b^3)/a^12 + (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8) + (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 - (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2) - (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 - 72*A*C*a^10*b - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2))/(2*a^8) - (b^3*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*C*a^15*b)/a^12 + (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*2i)/(d*(a^7 - a^5*b^2))","B"
684,1,6465,271,13.255956,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^2),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^4+C\,b^4+2\,A\,a^2\,b^2-5\,C\,a^2\,b^2+3\,C\,a\,b^3-3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^4+C\,b^4+2\,A\,a^2\,b^2-5\,C\,a^2\,b^2-3\,C\,a\,b^3+3\,C\,a^3\,b\right)}{b^3\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,C\,a^4-C\,b^4+2\,A\,a^2\,b^2-3\,C\,a^2\,b^2\right)}{b\,\left(a\,b^2-b^3\right)\,\left(a+b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^4}-\frac{\left(\frac{\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{\left(\frac{\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}+\frac{\left(\frac{\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}}\right)\,\left(3\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^5*(6*C*a^4 + C*b^4 + 2*A*a^2*b^2 - 5*C*a^2*b^2 + 3*C*a*b^3 - 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (tan(c/2 + (d*x)/2)*(6*C*a^4 + C*b^4 + 2*A*a^2*b^2 - 5*C*a^2*b^2 - 3*C*a*b^3 + 3*C*a^3*b))/(b^3*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)^3*(6*C*a^4 - C*b^4 + 2*A*a^2*b^2 - 3*C*a^2*b^2))/(b*(a*b^2 - b^3)*(a + b)))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(3*a + b) - tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) - (atan(-(((((3*C*a^2 + b^2*(A + C/2))*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/b^4 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2))*1i)/b^4 - ((((3*C*a^2 + b^2*(A + C/2))*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/b^4 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2))*1i)/b^4)/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + ((((3*C*a^2 + b^2*(A + C/2))*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/b^4 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2)))/b^4 + ((((3*C*a^2 + b^2*(A + C/2))*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/b^4 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2)))/b^4))*(3*C*a^2 + b^2*(A + C/2))*2i)/(b^4*d) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
685,1,4105,153,12.168891,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^2),x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^3+C\,b^3+A\,a\,b^2-C\,a\,b^2-C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a^3-C\,b^3+A\,a\,b^2-C\,a\,b^2+C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{C\,a\,\mathrm{atan}\left(\frac{\frac{C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{2\,C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{64\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}\right)\,2{}\mathrm{i}}{b^3}+\frac{C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{2\,C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{64\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}\right)\,2{}\mathrm{i}}{b^3}}{\frac{64\,\left(2\,A^2\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{2\,C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{2\,C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{64\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}\right)}{b^3}-\frac{2\,C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{2\,C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{64\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}\right)}{b^3}}\right)\,4{}\mathrm{i}}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(2\,A^2\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"(C*a*atan(((C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (2*C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (64*C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3)*2i)/b^3 + (C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (2*C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (64*C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3)*2i)/b^3)/((64*(8*C^3*a^8 - 4*C^3*a^7*b + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 2*A^2*C*a*b^7 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (2*C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (2*C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (64*C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3))/b^3 - (2*C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (2*C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (64*C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3))/b^3))*4i)/(b^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(2*C*a^3 + C*b^3 + A*a*b^2 - C*a*b^2 - C*a^2*b))/(b^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)*(2*C*a^3 - C*b^3 + A*a*b^2 - C*a*b^2 + C*a^2*b))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) - 2*a*tan(c/2 + (d*x)/2)^2)) + (atan(((((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*C^3*a^8 - 4*C^3*a^7*b + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 2*A^2*C*a*b^7 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
686,1,3838,135,11.219431,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^2),x)","-\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)\,1{}\mathrm{i}}{b^2}-\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)\,1{}\mathrm{i}}{b^2}}{\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)}{b^2}-\frac{64\,\left(A^2\,C\,a^2\,b^3-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)}{b^2}}\right)\,2{}\mathrm{i}}{b^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"- (C*atan(((C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 - (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 - (C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 + (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2)/((C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 - (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2 - (64*(C^3*a^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 + (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2))*2i)/(b^2*d) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2))/(d*(a + b)*(a*b - b^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b))) - (a*atan(((a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(C^3*a^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))","B"
687,1,3850,125,11.223999,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^2,x)","\frac{2\,A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)}{a^2}-\frac{A\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)}{a^2}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{A\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"(2*A*atan(((A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 + (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2 - (A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 - (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2)/((64*(A^3*b^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - A^2*C*a*b^4 + A^2*C*a^4*b + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 + (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 + (A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 - (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)))/(a^2*d) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2))/(d*(a + b)*(a*b - a^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b))) + (b*atan(((b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(A^3*b^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - A^2*C*a*b^4 + A^2*C*a^4*b + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) - (b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))","B"
688,1,4113,171,11.666869,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^3+2\,A\,b^3-A\,a\,b^2-A\,a^2\,b+C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-A\,a^3+A\,a\,b^2-A\,a^2\,b+C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{4\,A\,b\,\mathrm{atan}\left(\frac{\frac{2\,A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{a^3}\right)}{a^3}+\frac{2\,A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{a^3}\right)}{a^3}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+2\,A\,C^2\,a^7\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{a^3}\right)\,2{}\mathrm{i}}{a^3}-\frac{A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{a^3}\right)\,2{}\mathrm{i}}{a^3}}\right)}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+2\,A\,C^2\,a^7\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)^3*(A*a^3 + 2*A*b^3 - A*a*b^2 - A*a^2*b + C*a^2*b))/(a^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(2*A*b^3 - A*a^3 + A*a*b^2 - A*a^2*b + C*a^2*b))/(a^2*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) + 2*b*tan(c/2 + (d*x)/2)^2)) - (4*A*b*atan(((2*A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/a^3))/a^3 + (2*A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/a^3))/a^3)/((64*(8*A^3*b^8 - 4*A^3*a*b^7 - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 + 2*A*C^2*a^7*b - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/a^3)*2i)/a^3 - (A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/a^3)*2i)/a^3)))/(a^3*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*A^3*b^8 - 4*A^3*a*b^7 - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 + 2*A*C^2*a^7*b - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) - (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
689,1,6519,256,13.266937,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^4+6\,A\,b^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2+3\,A\,a\,b^3-3\,A\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A\,a^4+6\,A\,b^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,A\,a\,b^3+3\,A\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^4-6\,A\,b^4+3\,A\,a^2\,b^2-2\,C\,a^2\,b^2\right)}{a\,\left(a^2\,b-a^3\right)\,\left(a+b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(a+3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)}{a^4}\right)}{a^4}+\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)}{a^4}\right)}{a^4}}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+3{}\mathrm{i}\,A\,b^2\right)\,2{}\mathrm{i}}{a^4\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"(atan((((A*b^2*3i + a^2*((A*1i)/2 + C*1i))*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i)))/a^4)*1i)/a^4 + ((A*b^2*3i + a^2*((A*1i)/2 + C*1i))*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i)))/a^4)*1i)/a^4)/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - ((A*b^2*3i + a^2*((A*1i)/2 + C*1i))*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i)))/a^4))/a^4 + ((A*b^2*3i + a^2*((A*1i)/2 + C*1i))*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i)))/a^4))/a^4))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i))*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)*(A*a^4 + 6*A*b^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 + 3*A*a*b^3 - 3*A*a^3*b))/((a^3*b - a^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(A*a^4 + 6*A*b^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*A*a*b^3 + 3*A*a^3*b))/((a^3*b - a^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(A*a^4 - 6*A*b^4 + 3*A*a^2*b^2 - 2*C*a^2*b^2))/(a*(a^2*b - a^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) - tan(c/2 + (d*x)/2)^6*(a - b))) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
690,1,6978,326,13.698086,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^5+36\,A\,b^5-3\,C\,a^5-19\,A\,a^2\,b^3-7\,A\,a^3\,b^2+18\,C\,a^2\,b^3+3\,C\,a^3\,b^2+6\,A\,a\,b^4-8\,A\,a^4\,b-9\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A\,a^5-36\,A\,b^5-3\,C\,a^5+19\,A\,a^2\,b^3-7\,A\,a^3\,b^2-18\,C\,a^2\,b^3+3\,C\,a^3\,b^2+6\,A\,a\,b^4+8\,A\,a^4\,b+9\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,a^5+4\,A\,b^5+C\,a^5-3\,A\,a^2\,b^3+A\,a^3\,b^2+2\,C\,a^2\,b^3-C\,a^3\,b^2-2\,A\,a\,b^4-C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^5-4\,A\,b^5+C\,a^5+3\,A\,a^2\,b^3+A\,a^3\,b^2-2\,C\,a^2\,b^3-C\,a^3\,b^2-2\,A\,a\,b^4+C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,b-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(2\,a+4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)}{a^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)}{a^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^5}}{-\frac{64\,\left(5\,A^3\,a^8\,b^6-5\,A^3\,a^7\,b^7+31\,A^3\,a^6\,b^8-6\,A^3\,a^5\,b^9+12\,A^3\,a^4\,b^{10}+48\,A^3\,a^3\,b^{11}-112\,A^3\,a^2\,b^{12}-32\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+3\,A^2\,C\,a^{10}\,b^4-3\,A^2\,C\,a^9\,b^5+39\,A^2\,C\,a^8\,b^6-9\,A^2\,C\,a^7\,b^7+54\,A^2\,C\,a^6\,b^8+72\,A^2\,C\,a^5\,b^9-192\,A^2\,C\,a^4\,b^{10}-48\,A^2\,C\,a^3\,b^{11}+96\,A^2\,C\,a^2\,b^{12}+12\,A\,C^2\,a^{10}\,b^4-3\,A\,C^2\,a^9\,b^5+48\,A\,C^2\,a^8\,b^6+36\,A\,C^2\,a^7\,b^7-108\,A\,C^2\,a^6\,b^8-24\,A\,C^2\,a^5\,b^9+48\,A\,C^2\,a^4\,b^{10}+12\,C^3\,a^{10}\,b^4+6\,C^3\,a^9\,b^5-20\,C^3\,a^8\,b^6-4\,C^3\,a^7\,b^7+8\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)}{a^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)}{a^5}+\frac{\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)}{a^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)}{a^5}}\right)\,\left(A\,b^3\,4{}\mathrm{i}+a^2\,b\,\left(A+2\,C\right)\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}{\frac{64\,\left(5\,A^3\,a^8\,b^6-5\,A^3\,a^7\,b^7+31\,A^3\,a^6\,b^8-6\,A^3\,a^5\,b^9+12\,A^3\,a^4\,b^{10}+48\,A^3\,a^3\,b^{11}-112\,A^3\,a^2\,b^{12}-32\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+3\,A^2\,C\,a^{10}\,b^4-3\,A^2\,C\,a^9\,b^5+39\,A^2\,C\,a^8\,b^6-9\,A^2\,C\,a^7\,b^7+54\,A^2\,C\,a^6\,b^8+72\,A^2\,C\,a^5\,b^9-192\,A^2\,C\,a^4\,b^{10}-48\,A^2\,C\,a^3\,b^{11}+96\,A^2\,C\,a^2\,b^{12}+12\,A\,C^2\,a^{10}\,b^4-3\,A\,C^2\,a^9\,b^5+48\,A\,C^2\,a^8\,b^6+36\,A\,C^2\,a^7\,b^7-108\,A\,C^2\,a^6\,b^8-24\,A\,C^2\,a^5\,b^9+48\,A\,C^2\,a^4\,b^{10}+12\,C^3\,a^{10}\,b^4+6\,C^3\,a^9\,b^5-20\,C^3\,a^8\,b^6-4\,C^3\,a^7\,b^7+8\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)^3*(A*a^5 + 36*A*b^5 - 3*C*a^5 - 19*A*a^2*b^3 - 7*A*a^3*b^2 + 18*C*a^2*b^3 + 3*C*a^3*b^2 + 6*A*a*b^4 - 8*A*a^4*b - 9*C*a^4*b))/(3*a^4*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)^5*(A*a^5 - 36*A*b^5 - 3*C*a^5 + 19*A*a^2*b^3 - 7*A*a^3*b^2 - 18*C*a^2*b^3 + 3*C*a^3*b^2 + 6*A*a*b^4 + 8*A*a^4*b + 9*C*a^4*b))/(3*a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^7*(A*a^5 + 4*A*b^5 + C*a^5 - 3*A*a^2*b^3 + A*a^3*b^2 + 2*C*a^2*b^3 - C*a^3*b^2 - 2*A*a*b^4 - C*a^4*b))/(a^4*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)*(A*a^5 - 4*A*b^5 + C*a^5 + 3*A*a^2*b^3 + A*a^3*b^2 - 2*C*a^2*b^3 - C*a^3*b^2 - 2*A*a*b^4 + C*a^4*b))/(a^4*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^8*(a - b) + tan(c/2 + (d*x)/2)^2*(2*a + 4*b) - tan(c/2 + (d*x)/2)^6*(2*a - 4*b) + 6*b*tan(c/2 + (d*x)/2)^4)) - (atan(-((((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*tan(c/2 + (d*x)/2)*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i + a^2*b*(A + 2*C)*1i))/a^5 + (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*1i)/a^5 - (((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*tan(c/2 + (d*x)/2)*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i + a^2*b*(A + 2*C)*1i))/a^5 - (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*1i)/a^5)/((((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*tan(c/2 + (d*x)/2)*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i + a^2*b*(A + 2*C)*1i))/a^5 + (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i + a^2*b*(A + 2*C)*1i))/a^5 - (64*(64*A^3*b^14 - 32*A^3*a*b^13 - 112*A^3*a^2*b^12 + 48*A^3*a^3*b^11 + 12*A^3*a^4*b^10 - 6*A^3*a^5*b^9 + 31*A^3*a^6*b^8 - 5*A^3*a^7*b^7 + 5*A^3*a^8*b^6 + 8*C^3*a^6*b^8 - 4*C^3*a^7*b^7 - 20*C^3*a^8*b^6 + 6*C^3*a^9*b^5 + 12*C^3*a^10*b^4 + 48*A*C^2*a^4*b^10 - 24*A*C^2*a^5*b^9 - 108*A*C^2*a^6*b^8 + 36*A*C^2*a^7*b^7 + 48*A*C^2*a^8*b^6 - 3*A*C^2*a^9*b^5 + 12*A*C^2*a^10*b^4 + 96*A^2*C*a^2*b^12 - 48*A^2*C*a^3*b^11 - 192*A^2*C*a^4*b^10 + 72*A^2*C*a^5*b^9 + 54*A^2*C*a^6*b^8 - 9*A^2*C*a^7*b^7 + 39*A^2*C*a^8*b^6 - 3*A^2*C*a^9*b^5 + 3*A^2*C*a^10*b^4))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*tan(c/2 + (d*x)/2)*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i + a^2*b*(A + 2*C)*1i))/a^5 - (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i + a^2*b*(A + 2*C)*1i))/a^5))*(A*b^3*4i + a^2*b*(A + 2*C)*1i)*2i)/(a^5*d) - (b^2*atan(((b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))/((64*(64*A^3*b^14 - 32*A^3*a*b^13 - 112*A^3*a^2*b^12 + 48*A^3*a^3*b^11 + 12*A^3*a^4*b^10 - 6*A^3*a^5*b^9 + 31*A^3*a^6*b^8 - 5*A^3*a^7*b^7 + 5*A^3*a^8*b^6 + 8*C^3*a^6*b^8 - 4*C^3*a^7*b^7 - 20*C^3*a^8*b^6 + 6*C^3*a^9*b^5 + 12*C^3*a^10*b^4 + 48*A*C^2*a^4*b^10 - 24*A*C^2*a^5*b^9 - 108*A*C^2*a^6*b^8 + 36*A*C^2*a^7*b^7 + 48*A*C^2*a^8*b^6 - 3*A*C^2*a^9*b^5 + 12*A*C^2*a^10*b^4 + 96*A^2*C*a^2*b^12 - 48*A^2*C*a^3*b^11 - 192*A^2*C*a^4*b^10 + 72*A^2*C*a^5*b^9 + 54*A^2*C*a^6*b^8 - 9*A^2*C*a^7*b^7 + 39*A^2*C*a^8*b^6 - 3*A^2*C*a^9*b^5 + 3*A^2*C*a^10*b^4))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*2i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
691,1,10408,381,18.474172,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b/cos(c + d*x))^3),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,C\,a^6-C\,b^6-6\,A\,a^2\,b^4+A\,a^3\,b^3+2\,A\,a^4\,b^2+8\,C\,a^2\,b^4-10\,C\,a^3\,b^3-23\,C\,a^4\,b^2+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,C\,a^7+3\,C\,b^7-6\,A\,a^2\,b^5-15\,A\,a^3\,b^4+3\,A\,a^4\,b^3+6\,A\,a^5\,b^2+5\,C\,a^2\,b^5+26\,C\,a^3\,b^4-29\,C\,a^4\,b^3-67\,C\,a^5\,b^2-4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,C\,b^7-36\,C\,a^7-6\,A\,a^2\,b^5+15\,A\,a^3\,b^4+3\,A\,a^4\,b^3-6\,A\,a^5\,b^2+5\,C\,a^2\,b^5-26\,C\,a^3\,b^4-29\,C\,a^4\,b^3+67\,C\,a^5\,b^2+4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(C\,b^6-12\,C\,a^6+6\,A\,a^2\,b^4+A\,a^3\,b^3-2\,A\,a^4\,b^2-8\,C\,a^2\,b^4-10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a\,b^4-b^5\right)\,{\left(a+b\right)}^2}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b\,a\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^5}}{\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^5}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^5}}\right)\,\left(6\,C\,a^2+\left(A+\frac{C}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^5\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}{\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(12*C*a^6 - C*b^6 - 6*A*a^2*b^4 + A*a^3*b^3 + 2*A*a^4*b^2 + 8*C*a^2*b^4 - 10*C*a^3*b^3 - 23*C*a^4*b^2 + 5*C*a*b^5 + 6*C*a^5*b))/((a + b)*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^3*(36*C*a^7 + 3*C*b^7 - 6*A*a^2*b^5 - 15*A*a^3*b^4 + 3*A*a^4*b^3 + 6*A*a^5*b^2 + 5*C*a^2*b^5 + 26*C*a^3*b^4 - 29*C*a^4*b^3 - 67*C*a^5*b^2 - 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^5*(3*C*b^7 - 36*C*a^7 - 6*A*a^2*b^5 + 15*A*a^3*b^4 + 3*A*a^4*b^3 - 6*A*a^5*b^2 + 5*C*a^2*b^5 - 26*C*a^3*b^4 - 29*C*a^4*b^3 + 67*C*a^5*b^2 + 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^7*(C*b^6 - 12*C*a^6 + 6*A*a^2*b^4 + A*a^3*b^3 - 2*A*a^4*b^2 - 8*C*a^2*b^4 - 10*C*a^3*b^3 + 23*C*a^4*b^2 + 5*C*a*b^5 + 6*C*a^5*b))/((a*b^4 - b^5)*(a + b)^2))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(6*a^2 - 2*b^2) - tan(c/2 + (d*x)/2)^2*(4*a*b + 4*a^2) + tan(c/2 + (d*x)/2)^6*(4*a*b - 4*a^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + ((6*C*a^2 + b^2*(A + C/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5)*(6*C*a^2 + b^2*(A + C/2))*1i)/b^5 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - ((6*C*a^2 + b^2*(A + C/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5)*(6*C*a^2 + b^2*(A + C/2))*1i)/b^5)/((8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + ((6*C*a^2 + b^2*(A + C/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5)*(6*C*a^2 + b^2*(A + C/2)))/b^5 - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - ((6*C*a^2 + b^2*(A + C/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5)*(6*C*a^2 + b^2*(A + C/2)))/b^5))*(6*C*a^2 + b^2*(A + C/2))*2i)/(b^5*d) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*((a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*((a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*((a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*((a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*1i)/(d*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))","B"
692,1,7197,271,13.524553,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^3),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^5+2\,C\,b^5+A\,a^2\,b^3-4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-4\,A\,a\,b^4+2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,b^5-6\,C\,a^5+A\,a^2\,b^3-4\,C\,a^2\,b^3+12\,C\,a^3\,b^2+4\,A\,a\,b^4-2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,b^6-6\,C\,a^6+3\,A\,a^2\,b^4-6\,C\,a^2\,b^4+13\,C\,a^4\,b^2\right)}{b\,\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}+\frac{C\,a\,\mathrm{atan}\left(\frac{\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{3\,C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{24\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)\,3{}\mathrm{i}}{b^4}+\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{3\,C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{24\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)\,3{}\mathrm{i}}{b^4}}{\frac{16\,\left(3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{3\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{3\,C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{24\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)}{b^4}-\frac{3\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{3\,C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{24\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)}{b^4}}\right)\,6{}\mathrm{i}}{b^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(6*C*a^5 + 2*C*b^5 + A*a^2*b^3 - 4*C*a^2*b^3 - 12*C*a^3*b^2 - 4*A*a*b^4 + 2*C*a*b^4 + 3*C*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) - (tan(c/2 + (d*x)/2)^5*(2*C*b^5 - 6*C*a^5 + A*a^2*b^3 - 4*C*a^2*b^3 + 12*C*a^3*b^2 + 4*A*a*b^4 - 2*C*a*b^4 + 3*C*a^4*b))/((a*b^3 - b^4)*(a + b)^2) + (2*tan(c/2 + (d*x)/2)^3*(2*C*b^6 - 6*C*a^6 + 3*A*a^2*b^4 - 6*C*a^2*b^4 + 13*C*a^4*b^2))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) + (C*a*atan(((C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (3*C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (24*C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4)*3i)/b^4 + (C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (3*C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (24*C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4)*3i)/b^4)/((16*(108*C^3*a^12 - 54*C^3*a^11*b + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 12*A^2*C*a*b^11 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (3*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (3*C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (24*C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4))/b^4 - (3*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (3*C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (24*C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4))/b^4))*6i)/(b^4*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(108*C^3*a^12 - 54*C^3*a^11*b + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 12*A^2*C*a*b^11 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*1i)/(d*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
693,1,6565,212,13.170167,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2+6\,C\,a^2\,b^2+A\,a\,b^3+C\,a^3\,b\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2+6\,C\,a^2\,b^2-A\,a\,b^3-C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)\,1{}\mathrm{i}}{b^3}-\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)}{b^3}+\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)}{b^3}}\right)\,2{}\mathrm{i}}{b^3\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"(C*atan(((C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3 - (C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3)/((16*(4*C^3*a^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 + (C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3))*2i)/(b^3*d) - ((tan(c/2 + (d*x)/2)^3*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 + 6*C*a^2*b^2 + A*a*b^3 + C*a^3*b))/((a*b^2 - b^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 + 6*C*a^2*b^2 - A*a*b^3 - C*a^3*b))/((a + b)*(b^4 - 2*a*b^3 + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(4*C^3*a^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*((a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*1i)/(d*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
694,1,241,177,6.561701,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^3),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^2+C\,a^2-4\,A\,a\,b-4\,C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^2+C\,a^2+4\,A\,a\,b+4\,C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,A\,a^2+A\,b^2+C\,a^2+2\,C\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 - 4*A*a*b - 4*C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^3*(A*b^2 + C*a^2 + 4*A*a*b + 4*C*a*b))/((a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atanh((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*A*a^2 + A*b^2 + C*a^2 + 2*C*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
695,1,6574,202,14.243309,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^4-2\,A\,b^4+6\,A\,a^2\,b^2+2\,C\,a^2\,b^2+A\,a\,b^3+C\,a^3\,b\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4-6\,A\,a^2\,b^2-2\,C\,a^2\,b^2+A\,a\,b^3+C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{2\,A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)}{a^3}-\frac{A\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)}{a^3}}{-\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{A\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}\right)}{a^3\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*C*a^4 - 2*A*b^4 + 6*A*a^2*b^2 + 2*C*a^2*b^2 + A*a*b^3 + C*a^3*b))/((a^2*b - a^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 - 6*A*a^2*b^2 - 2*C*a^2*b^2 + A*a*b^3 + C*a^3*b))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (2*A*atan(((A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 - (A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 - (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3)/((A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3 - (16*(4*A^3*b^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 + 6*A^2*C*a^8*b + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 - (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3)))/(a^3*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(4*A^3*b^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 + 6*A^2*C*a^8*b + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
696,1,7202,266,14.148598,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^5+6\,A\,b^5-12\,A\,a^2\,b^3-4\,A\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4+2\,A\,a^4\,b-4\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^5-6\,A\,b^5+12\,A\,a^2\,b^3-4\,A\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4-2\,A\,a^4\,b+4\,C\,a^4\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^6-6\,A\,b^6+13\,A\,a^2\,b^4-6\,A\,a^4\,b^2+3\,C\,a^4\,b^2\right)}{a\,\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}-\frac{6\,A\,b\,\mathrm{atan}\left(\frac{\frac{3\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)\,24{}\mathrm{i}}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,3{}\mathrm{i}}{a^4}\right)}{a^4}+\frac{3\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)\,24{}\mathrm{i}}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,3{}\mathrm{i}}{a^4}\right)}{a^4}}{\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)\,24{}\mathrm{i}}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,3{}\mathrm{i}}{a^4}\right)\,3{}\mathrm{i}}{a^4}-\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)\,24{}\mathrm{i}}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,3{}\mathrm{i}}{a^4}\right)\,3{}\mathrm{i}}{a^4}}\right)}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^5 + 6*A*b^5 - 12*A*a^2*b^3 - 4*A*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 + 2*A*a^4*b - 4*C*a^4*b))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) - (tan(c/2 + (d*x)/2)^5*(2*A*a^5 - 6*A*b^5 + 12*A*a^2*b^3 - 4*A*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 - 2*A*a^4*b + 4*C*a^4*b))/((a^3*b - a^4)*(a + b)^2) + (2*tan(c/2 + (d*x)/2)^3*(2*A*a^6 - 6*A*b^6 + 13*A*a^2*b^4 - 6*A*a^4*b^2 + 3*C*a^4*b^2))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) - (6*A*b*atan(((3*A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2)*24i)/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*3i)/a^4))/a^4 + (3*A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2)*24i)/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*3i)/a^4))/a^4)/((16*(108*A^3*b^12 - 54*A^3*a*b^11 - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 + 12*A*C^2*a^11*b + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2)*24i)/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*3i)/a^4)*3i)/a^4 - (A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2)*24i)/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*3i)/a^4)*3i)/a^4)))/(a^4*d) - (atan(((((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((16*(108*A^3*b^12 - 54*A^3*a*b^11 - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 + 12*A*C^2*a^11*b + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*1i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
697,1,10471,369,17.744571,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A\,b^6-A\,a^6-23\,A\,a^2\,b^4-10\,A\,a^3\,b^3+8\,A\,a^4\,b^2+2\,C\,a^2\,b^4+C\,a^3\,b^3-6\,C\,a^4\,b^2+6\,A\,a\,b^5+5\,A\,a^5\,b\right)}{\left(a+b\right)\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^7+36\,A\,b^7-67\,A\,a^2\,b^5-29\,A\,a^3\,b^4+26\,A\,a^4\,b^3+5\,A\,a^5\,b^2+6\,C\,a^2\,b^5+3\,C\,a^3\,b^4-15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6-4\,A\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A\,a^7-36\,A\,b^7+67\,A\,a^2\,b^5-29\,A\,a^3\,b^4-26\,A\,a^4\,b^3+5\,A\,a^5\,b^2-6\,C\,a^2\,b^5+3\,C\,a^3\,b^4+15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6+4\,A\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,a^6-12\,A\,b^6+23\,A\,a^2\,b^4-10\,A\,a^3\,b^3-8\,A\,a^4\,b^2-2\,C\,a^2\,b^4+C\,a^3\,b^3+6\,C\,a^4\,b^2+6\,A\,a\,b^5+5\,A\,a^5\,b\right)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^2}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-6\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,b^2+4\,a\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,1{}\mathrm{i}}{a^5}}{-\frac{8\,\left(20\,A^3\,a^{12}\,b^3-20\,A^3\,a^{11}\,b^4+411\,A^3\,a^{10}\,b^5-11\,A^3\,a^9\,b^6+1314\,A^3\,a^8\,b^7+2326\,A^3\,a^7\,b^8-7829\,A^3\,a^6\,b^9-4770\,A^3\,a^5\,b^{10}+11700\,A^3\,a^4\,b^{11}+3456\,A^3\,a^3\,b^{12}-7344\,A^3\,a^2\,b^{13}-864\,A^3\,a\,b^{14}+1728\,A^3\,b^{15}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)}{a^5}+\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)}{a^5}}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+6{}\mathrm{i}\,A\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}{\frac{8\,\left(20\,A^3\,a^{12}\,b^3-20\,A^3\,a^{11}\,b^4+411\,A^3\,a^{10}\,b^5-11\,A^3\,a^9\,b^6+1314\,A^3\,a^8\,b^7+2326\,A^3\,a^7\,b^8-7829\,A^3\,a^6\,b^9-4770\,A^3\,a^5\,b^{10}+11700\,A^3\,a^4\,b^{11}+3456\,A^3\,a^3\,b^{12}-7344\,A^3\,a^2\,b^{13}-864\,A^3\,a\,b^{14}+1728\,A^3\,b^{15}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}","Not used",1,"(b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*((a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*((a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*((a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*((a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*1i)/(d*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) - (atan((((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5 + (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*1i)/a^5 - ((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5 - (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*1i)/a^5)/(((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5 + (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))/a^5 - (8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + ((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*6i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5 - (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))/a^5))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i))*2i)/(a^5*d) - ((tan(c/2 + (d*x)/2)*(12*A*b^6 - A*a^6 - 23*A*a^2*b^4 - 10*A*a^3*b^3 + 8*A*a^4*b^2 + 2*C*a^2*b^4 + C*a^3*b^3 - 6*C*a^4*b^2 + 6*A*a*b^5 + 5*A*a^5*b))/((a + b)*(a^6 - 2*a^5*b + a^4*b^2)) + (tan(c/2 + (d*x)/2)^3*(3*A*a^7 + 36*A*b^7 - 67*A*a^2*b^5 - 29*A*a^3*b^4 + 26*A*a^4*b^3 + 5*A*a^5*b^2 + 6*C*a^2*b^5 + 3*C*a^3*b^4 - 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 - 4*A*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^5*(3*A*a^7 - 36*A*b^7 + 67*A*a^2*b^5 - 29*A*a^3*b^4 - 26*A*a^4*b^3 + 5*A*a^5*b^2 - 6*C*a^2*b^5 + 3*C*a^3*b^4 + 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 + 4*A*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^7*(A*a^6 - 12*A*b^6 + 23*A*a^2*b^4 - 10*A*a^3*b^3 - 8*A*a^4*b^2 - 2*C*a^2*b^4 + C*a^3*b^3 + 6*C*a^4*b^2 + 6*A*a*b^5 + 5*A*a^5*b))/((a^4*b - a^5)*(a + b)^2))/(d*(2*a*b - tan(c/2 + (d*x)/2)^4*(2*a^2 - 6*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*b^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
698,1,10065,378,17.155000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b/cos(c + d*x))^4),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6-7\,A\,a^3\,b^5+10\,A\,a^4\,b^4-72\,C\,a^2\,b^6-60\,C\,a^3\,b^5+273\,C\,a^4\,b^4+47\,C\,a^5\,b^3-236\,C\,a^6\,b^2-18\,A\,a\,b^7-12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6+7\,A\,a^3\,b^5+10\,A\,a^4\,b^4-72\,C\,a^2\,b^6+60\,C\,a^3\,b^5+273\,C\,a^4\,b^4-47\,C\,a^5\,b^3-236\,C\,a^6\,b^2+18\,A\,a\,b^7+12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,C\,a^7-2\,C\,b^7-3\,A\,a^2\,b^5+2\,A\,a^3\,b^4+6\,C\,a^2\,b^5+26\,C\,a^3\,b^4-11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,C\,a\,b^6+4\,C\,a^6\,b\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,C\,a^7+2\,C\,b^7+3\,A\,a^2\,b^5+2\,A\,a^3\,b^4-6\,C\,a^2\,b^5+26\,C\,a^3\,b^4+11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,C\,a\,b^6-4\,C\,a^6\,b\right)}{b^4\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a\,b^2-6\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3+6\,a^2\,b-2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3-6\,a^2\,b+2\,b^3\right)+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{C\,a\,\mathrm{atan}\left(\frac{\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{32\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)}{b^5}\right)\,4{}\mathrm{i}}{b^5}+\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{32\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)}{b^5}\right)\,4{}\mathrm{i}}{b^5}}{\frac{32\,\left(18\,A^2\,C\,a^5\,b^{11}+24\,A^2\,C\,a^3\,b^{13}+8\,A^2\,C\,a\,b^{15}-48\,A\,C^2\,a^{11}\,b^5-48\,A\,C^2\,a^{10}\,b^6+160\,A\,C^2\,a^9\,b^7+112\,A\,C^2\,a^8\,b^8-148\,A\,C^2\,a^7\,b^9-48\,A\,C^2\,a^6\,b^{10}+8\,A\,C^2\,a^5\,b^{11}-48\,A\,C^2\,a^4\,b^{12}+128\,A\,C^2\,a^3\,b^{13}+32\,A\,C^2\,a^2\,b^{14}+128\,C^3\,a^{16}-64\,C^3\,a^{15}\,b-832\,C^3\,a^{14}\,b^2+400\,C^3\,a^{13}\,b^3+2288\,C^3\,a^{12}\,b^4-1088\,C^3\,a^{11}\,b^5-3472\,C^3\,a^{10}\,b^6+1602\,C^3\,a^9\,b^7+3088\,C^3\,a^8\,b^8-1280\,C^3\,a^7\,b^9-1520\,C^3\,a^6\,b^{10}+480\,C^3\,a^5\,b^{11}+320\,C^3\,a^4\,b^{12}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{32\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)}{b^5}\right)}{b^5}-\frac{4\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{32\,C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)}{b^5}\right)}{b^5}}\right)\,8{}\mathrm{i}}{b^5\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}{\frac{32\,\left(18\,A^2\,C\,a^5\,b^{11}+24\,A^2\,C\,a^3\,b^{13}+8\,A^2\,C\,a\,b^{15}-48\,A\,C^2\,a^{11}\,b^5-48\,A\,C^2\,a^{10}\,b^6+160\,A\,C^2\,a^9\,b^7+112\,A\,C^2\,a^8\,b^8-148\,A\,C^2\,a^7\,b^9-48\,A\,C^2\,a^6\,b^{10}+8\,A\,C^2\,a^5\,b^{11}-48\,A\,C^2\,a^4\,b^{12}+128\,A\,C^2\,a^3\,b^{13}+32\,A\,C^2\,a^2\,b^{14}+128\,C^3\,a^{16}-64\,C^3\,a^{15}\,b-832\,C^3\,a^{14}\,b^2+400\,C^3\,a^{13}\,b^3+2288\,C^3\,a^{12}\,b^4-1088\,C^3\,a^{11}\,b^5-3472\,C^3\,a^{10}\,b^6+1602\,C^3\,a^9\,b^7+3088\,C^3\,a^8\,b^8-1280\,C^3\,a^7\,b^9-1520\,C^3\,a^6\,b^{10}+480\,C^3\,a^5\,b^{11}+320\,C^3\,a^4\,b^{12}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}","Not used",1,"(C*a*atan(((C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (4*C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (32*C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8))))/b^5)*4i)/b^5 + (C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (4*C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (32*C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8))))/b^5)*4i)/b^5)/((32*(128*C^3*a^16 - 64*C^3*a^15*b + 320*C^3*a^4*b^12 + 480*C^3*a^5*b^11 - 1520*C^3*a^6*b^10 - 1280*C^3*a^7*b^9 + 3088*C^3*a^8*b^8 + 1602*C^3*a^9*b^7 - 3472*C^3*a^10*b^6 - 1088*C^3*a^11*b^5 + 2288*C^3*a^12*b^4 + 400*C^3*a^13*b^3 - 832*C^3*a^14*b^2 + 8*A^2*C*a*b^15 + 32*A*C^2*a^2*b^14 + 128*A*C^2*a^3*b^13 - 48*A*C^2*a^4*b^12 + 8*A*C^2*a^5*b^11 - 48*A*C^2*a^6*b^10 - 148*A*C^2*a^7*b^9 + 112*A*C^2*a^8*b^8 + 160*A*C^2*a^9*b^7 - 48*A*C^2*a^10*b^6 - 48*A*C^2*a^11*b^5 + 24*A^2*C*a^3*b^13 + 18*A^2*C*a^5*b^11))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (4*C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (32*C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8))))/b^5))/b^5 - (4*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (4*C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (32*C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8))))/b^5))/b^5))*8i)/(b^5*d) - ((tan(c/2 + (d*x)/2)^3*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 - 7*A*a^3*b^5 + 10*A*a^4*b^4 - 72*C*a^2*b^6 - 60*C*a^3*b^5 + 273*C*a^4*b^4 + 47*C*a^5*b^3 - 236*C*a^6*b^2 - 18*A*a*b^7 - 12*C*a^7*b))/(3*b^4*(a + b)^2*(a - b)^3) - (tan(c/2 + (d*x)/2)^5*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 + 7*A*a^3*b^5 + 10*A*a^4*b^4 - 72*C*a^2*b^6 + 60*C*a^3*b^5 + 273*C*a^4*b^4 - 47*C*a^5*b^3 - 236*C*a^6*b^2 + 18*A*a*b^7 + 12*C*a^7*b))/(3*b^4*(a + b)^3*(a - b)^2) - (tan(c/2 + (d*x)/2)*(8*C*a^7 - 2*C*b^7 - 3*A*a^2*b^5 + 2*A*a^3*b^4 + 6*C*a^2*b^5 + 26*C*a^3*b^4 - 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*C*a*b^6 + 4*C*a^6*b))/(b^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^7*(8*C*a^7 + 2*C*b^7 + 3*A*a^2*b^5 + 2*A*a^3*b^4 - 6*C*a^2*b^5 + 26*C*a^3*b^4 + 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*C*a*b^6 - 4*C*a^6*b))/(b^4*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^3) - tan(c/2 + (d*x)/2)^2*(6*a^2*b + 4*a^3 - 2*b^3) - tan(c/2 + (d*x)/2)^6*(4*a^3 - 6*a^2*b + 2*b^3) + a^3 + b^3 + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))/((32*(128*C^3*a^16 - 64*C^3*a^15*b + 320*C^3*a^4*b^12 + 480*C^3*a^5*b^11 - 1520*C^3*a^6*b^10 - 1280*C^3*a^7*b^9 + 3088*C^3*a^8*b^8 + 1602*C^3*a^9*b^7 - 3472*C^3*a^10*b^6 - 1088*C^3*a^11*b^5 + 2288*C^3*a^12*b^4 + 400*C^3*a^13*b^3 - 832*C^3*a^14*b^2 + 8*A^2*C*a*b^15 + 32*A*C^2*a^2*b^14 + 128*A*C^2*a^3*b^13 - 48*A*C^2*a^4*b^12 + 8*A*C^2*a^5*b^11 - 48*A*C^2*a^6*b^10 - 148*A*C^2*a^7*b^9 + 112*A*C^2*a^8*b^8 + 160*A*C^2*a^9*b^7 - 48*A*C^2*a^10*b^6 - 48*A*C^2*a^11*b^5 + 24*A^2*C*a^3*b^13 + 18*A^2*C*a^5*b^11))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*1i)/(d*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))","B"
699,1,9753,313,20.845298,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^4),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4-A\,a^3\,b^3+12\,C\,a^2\,b^4-4\,C\,a^3\,b^3-6\,C\,a^4\,b^2-2\,A\,a\,b^5+C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6+7\,A\,a^2\,b^4+18\,C\,a^2\,b^4-11\,C\,a^4\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4+A\,a^3\,b^3+12\,C\,a^2\,b^4+4\,C\,a^3\,b^3-6\,C\,a^4\,b^2+2\,A\,a\,b^5-C\,a^5\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)}{b^4}-\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)}{b^4}}\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 - A*a^3*b^3 + 12*C*a^2*b^4 - 4*C*a^3*b^3 - 6*C*a^4*b^2 - 2*A*a*b^5 + C*a^5*b))/((a + b)*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 + 7*A*a^2*b^4 + 18*C*a^2*b^4 - 11*C*a^4*b^2))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*b^3)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 + A*a^3*b^3 + 12*C*a^2*b^4 + 4*C*a^3*b^3 - 6*C*a^4*b^2 + 2*A*a*b^5 - C*a^5*b))/((a*b^3 - b^4)*(a + b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (C*atan(((C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4)*1i)/b^4 + (C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4)*1i)/b^4)/((16*(4*C^3*a^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4))/b^4 - (C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4))/b^4))*2i)/(b^4*d) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))/((16*(4*C^3*a^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))))*((a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*1i)/(d*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))","B"
700,1,482,261,8.294173,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^3+A\,b^3+2\,C\,a^3+6\,A\,a\,b^2+2\,A\,a^2\,b+6\,C\,a\,b^2+3\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^3+C\,a^3+7\,A\,a\,b^2+9\,C\,a\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^3-A\,b^3+2\,C\,a^3+6\,A\,a\,b^2-2\,A\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-4{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b+6{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2-4{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}{\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(4\,A\,a^2+A\,b^2+3\,C\,a^2+2\,C\,b^2\right)\,1{}\mathrm{i}}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(2*A*a^3 + A*b^3 + 2*C*a^3 + 6*A*a*b^2 + 2*A*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/((a + b)^3*(a - b)) - (4*tan(c/2 + (d*x)/2)^3*(3*A*a^3 + C*a^3 + 7*A*a*b^2 + 9*C*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)*(2*A*a^3 - A*b^3 + 2*C*a^3 + 6*A*a*b^2 - 2*A*a^2*b + 6*C*a*b^2 - 3*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (b*atan((a^4*tan(c/2 + (d*x)/2)*1i + b^4*tan(c/2 + (d*x)/2)*1i - a*b^3*tan(c/2 + (d*x)/2)*4i - a^3*b*tan(c/2 + (d*x)/2)*4i + a^2*b^2*tan(c/2 + (d*x)/2)*6i)/((a + b)^(1/2)*(a - b)^(7/2)))*(4*A*a^2 + A*b^2 + 3*C*a^2 + 2*C*b^2)*1i)/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
701,1,483,252,8.343445,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^4),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^3+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b+2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^3+3\,C\,b^3+9\,A\,a^2\,b+7\,C\,a^2\,b\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{a\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-4{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b+6{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2-4{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}{\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(2\,A\,a^2+3\,A\,b^2+C\,a^2+4\,C\,b^2\right)\,1{}\mathrm{i}}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"- ((tan(c/2 + (d*x)/2)^5*(2*A*b^3 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b + 2*C*a*b^2 + 6*C*a^2*b))/((a + b)^3*(a - b)) - (4*tan(c/2 + (d*x)/2)^3*(A*b^3 + 3*C*b^3 + 9*A*a^2*b + 7*C*a^2*b))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)*(2*A*b^3 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 2*C*a*b^2 + 6*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (a*atan((a^4*tan(c/2 + (d*x)/2)*1i + b^4*tan(c/2 + (d*x)/2)*1i - a*b^3*tan(c/2 + (d*x)/2)*4i - a^3*b*tan(c/2 + (d*x)/2)*4i + a^2*b^2*tan(c/2 + (d*x)/2)*6i)/((a + b)^(1/2)*(a - b)^(7/2)))*(2*A*a^2 + 3*A*b^2 + C*a^2 + 4*C*b^2)*1i)/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
702,1,9761,292,21.355582,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^4,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4-4\,A\,a^3\,b^3+12\,A\,a^4\,b^2-C\,a^3\,b^3+6\,C\,a^4\,b^2+A\,a\,b^5-2\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6-11\,A\,a^2\,b^4+18\,A\,a^4\,b^2+7\,C\,a^4\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4+4\,A\,a^3\,b^3+12\,A\,a^4\,b^2+C\,a^3\,b^3+6\,C\,a^4\,b^2-A\,a\,b^5+2\,C\,a^5\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{2\,A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)}{a^4}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)}{a^4}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}}\right)}{a^4\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}","Not used",1,"(2*A*atan(((A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4))/a^4 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4))/a^4)/((16*(4*A^3*b^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 + 8*A^2*C*a^12*b + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4)*1i)/a^4 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4)*1i)/a^4)))/(a^4*d) - ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 - 4*A*a^3*b^3 + 12*A*a^4*b^2 - C*a^3*b^3 + 6*C*a^4*b^2 + A*a*b^5 - 2*C*a^5*b))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 - 11*A*a^2*b^4 + 18*A*a^4*b^2 + 7*C*a^4*b^2))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 + 4*A*a^3*b^3 + 12*A*a^4*b^2 + C*a^3*b^3 + 6*C*a^4*b^2 - A*a*b^5 + 2*C*a^5*b))/((a^3*b - a^4)*(a + b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/((16*(4*A^3*b^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 + 8*A^2*C*a^12*b + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*1i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
703,1,10120,367,17.271123,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^4,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A\,b^7-2\,A\,a^7-24\,A\,a^2\,b^5-11\,A\,a^3\,b^4+26\,A\,a^4\,b^3+6\,A\,a^5\,b^2+2\,C\,a^4\,b^3-3\,C\,a^5\,b^2+4\,A\,a\,b^6-2\,A\,a^6\,b+6\,C\,a^6\,b\right)}{\left(a+b\right)\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^7+8\,A\,b^7-24\,A\,a^2\,b^5+11\,A\,a^3\,b^4+26\,A\,a^4\,b^3-6\,A\,a^5\,b^2+2\,C\,a^4\,b^3+3\,C\,a^5\,b^2-4\,A\,a\,b^6-2\,A\,a^6\,b+6\,C\,a^6\,b\right)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6+47\,A\,a^3\,b^5+273\,A\,a^4\,b^4-60\,A\,a^5\,b^3-72\,A\,a^6\,b^2+10\,C\,a^4\,b^4-7\,C\,a^5\,b^3+45\,C\,a^6\,b^2-12\,A\,a\,b^7-18\,C\,a^7\,b\right)}{3\,{\left(a+b\right)}^2\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6-47\,A\,a^3\,b^5+273\,A\,a^4\,b^4+60\,A\,a^5\,b^3-72\,A\,a^6\,b^2+10\,C\,a^4\,b^4+7\,C\,a^5\,b^3+45\,C\,a^6\,b^2+12\,A\,a\,b^7+18\,C\,a^7\,b\right)}{3\,\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2\,b-6\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^3+6\,a\,b^2+4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^3-6\,a\,b^2+4\,b^3\right)+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{8\,A\,b\,\mathrm{atan}\left(\frac{\frac{4\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)\,32{}\mathrm{i}}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,4{}\mathrm{i}}{a^5}\right)}{a^5}+\frac{4\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)\,32{}\mathrm{i}}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,4{}\mathrm{i}}{a^5}\right)}{a^5}}{\frac{32\,\left(320\,A^3\,a^{12}\,b^4+480\,A^3\,a^{11}\,b^5-1520\,A^3\,a^{10}\,b^6-1280\,A^3\,a^9\,b^7+3088\,A^3\,a^8\,b^8+1602\,A^3\,a^7\,b^9-3472\,A^3\,a^6\,b^{10}-1088\,A^3\,a^5\,b^{11}+2288\,A^3\,a^4\,b^{12}+400\,A^3\,a^3\,b^{13}-832\,A^3\,a^2\,b^{14}-64\,A^3\,a\,b^{15}+128\,A^3\,b^{16}+32\,A^2\,C\,a^{14}\,b^2+128\,A^2\,C\,a^{13}\,b^3-48\,A^2\,C\,a^{12}\,b^4+8\,A^2\,C\,a^{11}\,b^5-48\,A^2\,C\,a^{10}\,b^6-148\,A^2\,C\,a^9\,b^7+112\,A^2\,C\,a^8\,b^8+160\,A^2\,C\,a^7\,b^9-48\,A^2\,C\,a^6\,b^{10}-48\,A^2\,C\,a^5\,b^{11}+8\,A\,C^2\,a^{15}\,b+24\,A\,C^2\,a^{13}\,b^3+18\,A\,C^2\,a^{11}\,b^5\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)\,32{}\mathrm{i}}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,4{}\mathrm{i}}{a^5}\right)\,4{}\mathrm{i}}{a^5}-\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)\,32{}\mathrm{i}}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,4{}\mathrm{i}}{a^5}\right)\,4{}\mathrm{i}}{a^5}}\right)}{a^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}{\frac{32\,\left(320\,A^3\,a^{12}\,b^4+480\,A^3\,a^{11}\,b^5-1520\,A^3\,a^{10}\,b^6-1280\,A^3\,a^9\,b^7+3088\,A^3\,a^8\,b^8+1602\,A^3\,a^7\,b^9-3472\,A^3\,a^6\,b^{10}-1088\,A^3\,a^5\,b^{11}+2288\,A^3\,a^4\,b^{12}+400\,A^3\,a^3\,b^{13}-832\,A^3\,a^2\,b^{14}-64\,A^3\,a\,b^{15}+128\,A^3\,b^{16}+32\,A^2\,C\,a^{14}\,b^2+128\,A^2\,C\,a^{13}\,b^3-48\,A^2\,C\,a^{12}\,b^4+8\,A^2\,C\,a^{11}\,b^5-48\,A^2\,C\,a^{10}\,b^6-148\,A^2\,C\,a^9\,b^7+112\,A^2\,C\,a^8\,b^8+160\,A^2\,C\,a^7\,b^9-48\,A^2\,C\,a^6\,b^{10}-48\,A^2\,C\,a^5\,b^{11}+8\,A\,C^2\,a^{15}\,b+24\,A\,C^2\,a^{13}\,b^3+18\,A\,C^2\,a^{11}\,b^5\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(8*A*b^7 - 2*A*a^7 - 24*A*a^2*b^5 - 11*A*a^3*b^4 + 26*A*a^4*b^3 + 6*A*a^5*b^2 + 2*C*a^4*b^3 - 3*C*a^5*b^2 + 4*A*a*b^6 - 2*A*a^6*b + 6*C*a^6*b))/((a + b)*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)) + (tan(c/2 + (d*x)/2)^7*(2*A*a^7 + 8*A*b^7 - 24*A*a^2*b^5 + 11*A*a^3*b^4 + 26*A*a^4*b^3 - 6*A*a^5*b^2 + 2*C*a^4*b^3 + 3*C*a^5*b^2 - 4*A*a*b^6 - 2*A*a^6*b + 6*C*a^6*b))/((a^4*b - a^5)*(a + b)^3) + (tan(c/2 + (d*x)/2)^3*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 + 47*A*a^3*b^5 + 273*A*a^4*b^4 - 60*A*a^5*b^3 - 72*A*a^6*b^2 + 10*C*a^4*b^4 - 7*C*a^5*b^3 + 45*C*a^6*b^2 - 12*A*a*b^7 - 18*C*a^7*b))/(3*(a + b)^2*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)) - (tan(c/2 + (d*x)/2)^5*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 - 47*A*a^3*b^5 + 273*A*a^4*b^4 + 60*A*a^5*b^3 - 72*A*a^6*b^2 + 10*C*a^4*b^4 + 7*C*a^5*b^3 + 45*C*a^6*b^2 + 12*A*a*b^7 + 18*C*a^7*b))/(3*(a^4*b - a^5)*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a^2*b - 6*b^3) + tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 2*a^3 + 4*b^3) + tan(c/2 + (d*x)/2)^6*(2*a^3 - 6*a*b^2 + 4*b^3) + a^3 + b^3 - tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (8*A*b*atan(((4*A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2)*32i)/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*4i)/a^5))/a^5 + (4*A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2)*32i)/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*4i)/a^5))/a^5)/((32*(128*A^3*b^16 - 64*A^3*a*b^15 - 832*A^3*a^2*b^14 + 400*A^3*a^3*b^13 + 2288*A^3*a^4*b^12 - 1088*A^3*a^5*b^11 - 3472*A^3*a^6*b^10 + 1602*A^3*a^7*b^9 + 3088*A^3*a^8*b^8 - 1280*A^3*a^9*b^7 - 1520*A^3*a^10*b^6 + 480*A^3*a^11*b^5 + 320*A^3*a^12*b^4 + 8*A*C^2*a^15*b + 18*A*C^2*a^11*b^5 + 24*A*C^2*a^13*b^3 - 48*A^2*C*a^5*b^11 - 48*A^2*C*a^6*b^10 + 160*A^2*C*a^7*b^9 + 112*A^2*C*a^8*b^8 - 148*A^2*C*a^9*b^7 - 48*A^2*C*a^10*b^6 + 8*A^2*C*a^11*b^5 - 48*A^2*C*a^12*b^4 + 128*A^2*C*a^13*b^3 + 32*A^2*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2)*32i)/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*4i)/a^5)*4i)/a^5 - (A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2)*32i)/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*4i)/a^5)*4i)/a^5)))/(a^5*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))/((32*(128*A^3*b^16 - 64*A^3*a*b^15 - 832*A^3*a^2*b^14 + 400*A^3*a^3*b^13 + 2288*A^3*a^4*b^12 - 1088*A^3*a^5*b^11 - 3472*A^3*a^6*b^10 + 1602*A^3*a^7*b^9 + 3088*A^3*a^8*b^8 - 1280*A^3*a^9*b^7 - 1520*A^3*a^10*b^6 + 480*A^3*a^11*b^5 + 320*A^3*a^12*b^4 + 8*A*C^2*a^15*b + 18*A*C^2*a^11*b^5 + 24*A*C^2*a^13*b^3 - 48*A^2*C*a^5*b^11 - 48*A^2*C*a^6*b^10 + 160*A^2*C*a^7*b^9 + 112*A^2*C*a^8*b^8 - 148*A^2*C*a^9*b^7 - 48*A^2*C*a^10*b^6 + 8*A^2*C*a^11*b^5 - 48*A^2*C*a^12*b^4 + 128*A^2*C*a^13*b^3 + 32*A^2*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) - (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*1i)/(d*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))","B"
704,1,14266,513,23.991529,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^4,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^8+20\,A\,b^8-59\,A\,a^2\,b^6-27\,A\,a^3\,b^5+57\,A\,a^4\,b^4+21\,A\,a^5\,b^3-11\,A\,a^6\,b^2+2\,C\,a^2\,b^6+C\,a^3\,b^5-6\,C\,a^4\,b^4-4\,C\,a^5\,b^3+12\,C\,a^6\,b^2+10\,A\,a\,b^7-7\,A\,a^7\,b\right)}{a^5\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(A\,a^8+20\,A\,b^8-59\,A\,a^2\,b^6+27\,A\,a^3\,b^5+57\,A\,a^4\,b^4-21\,A\,a^5\,b^3-11\,A\,a^6\,b^2+2\,C\,a^2\,b^6-C\,a^3\,b^5-6\,C\,a^4\,b^4+4\,C\,a^5\,b^3+12\,C\,a^6\,b^2-10\,A\,a\,b^7+7\,A\,a^7\,b\right)}{a^5\,{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(120\,A\,b^9-6\,A\,a^9-364\,A\,a^2\,b^7-71\,A\,a^3\,b^6+369\,A\,a^4\,b^5+45\,A\,a^5\,b^4-111\,A\,a^6\,b^3-3\,A\,a^7\,b^2+12\,C\,a^2\,b^7+3\,C\,a^3\,b^6-37\,C\,a^4\,b^5-8\,C\,a^5\,b^4+60\,C\,a^6\,b^3+30\,A\,a\,b^8+21\,A\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,A\,a^9+120\,A\,b^9-364\,A\,a^2\,b^7+71\,A\,a^3\,b^6+369\,A\,a^4\,b^5-45\,A\,a^5\,b^4-111\,A\,a^6\,b^3+3\,A\,a^7\,b^2+12\,C\,a^2\,b^7-3\,C\,a^3\,b^6-37\,C\,a^4\,b^5+8\,C\,a^5\,b^4+60\,C\,a^6\,b^3-30\,A\,a\,b^8+21\,A\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^{10}+180\,A\,b^{10}-611\,A\,a^2\,b^8+740\,A\,a^4\,b^6-324\,A\,a^6\,b^4+36\,A\,a^8\,b^2+18\,C\,a^2\,b^8-62\,C\,a^4\,b^6+110\,C\,a^6\,b^4-36\,C\,a^8\,b^2\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^3+3\,a^2\,b+9\,a\,b^2+5\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^3-6\,a^2\,b+6\,a\,b^2+10\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-2\,a^3+6\,a^2\,b+6\,a\,b^2-10\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3+3\,a^2\,b-9\,a\,b^2+5\,b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,1{}\mathrm{i}}{a^6}-\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,1{}\mathrm{i}}{a^6}}{-\frac{8\,\left(40\,A^3\,a^{16}\,b^3-40\,A^3\,a^{15}\,b^4+1396\,A^3\,a^{14}\,b^5+204\,A^3\,a^{13}\,b^6+8281\,A^3\,a^{12}\,b^7+16999\,A^3\,a^{11}\,b^8-64479\,A^3\,a^{10}\,b^9-57345\,A^3\,a^9\,b^{10}+155991\,A^3\,a^8\,b^{11}+82337\,A^3\,a^7\,b^{12}-193689\,A^3\,a^6\,b^{13}-62030\,A^3\,a^5\,b^{14}+135260\,A^3\,a^4\,b^{15}+24400\,A^3\,a^3\,b^{16}-50800\,A^3\,a^2\,b^{17}-4000\,A^3\,a\,b^{18}+8000\,A^3\,b^{19}+8\,A^2\,C\,a^{18}\,b-8\,A^2\,C\,a^{17}\,b^2+448\,A^2\,C\,a^{16}\,b^3+192\,A^2\,C\,a^{15}\,b^4+4359\,A^2\,C\,a^{14}\,b^5+9657\,A^2\,C\,a^{13}\,b^6-25211\,A^2\,C\,a^{12}\,b^7-24901\,A^2\,C\,a^{11}\,b^8+53039\,A^2\,C\,a^{10}\,b^9+29513\,A^2\,C\,a^9\,b^{10}-60729\,A^2\,C\,a^8\,b^{11}-19233\,A^2\,C\,a^7\,b^{12}+41046\,A^2\,C\,a^6\,b^{13}+7080\,A^2\,C\,a^5\,b^{14}-15360\,A^2\,C\,a^4\,b^{15}-1200\,A^2\,C\,a^3\,b^{16}+2400\,A^2\,C\,a^2\,b^{17}+32\,A\,C^2\,a^{18}\,b+32\,A\,C^2\,a^{17}\,b^2+672\,A\,C^2\,a^{16}\,b^3+1760\,A\,C^2\,a^{15}\,b^4-3156\,A\,C^2\,a^{14}\,b^5-3196\,A\,C^2\,a^{13}\,b^6+5944\,A\,C^2\,a^{12}\,b^7+3448\,A\,C^2\,a^{11}\,b^8-6336\,A\,C^2\,a^{10}\,b^9-1983\,A\,C^2\,a^9\,b^{10}+4152\,A\,C^2\,a^8\,b^{11}+684\,A\,C^2\,a^7\,b^{12}-1548\,A\,C^2\,a^6\,b^{13}-120\,A\,C^2\,a^5\,b^{14}+240\,A\,C^2\,a^4\,b^{15}+32\,C^3\,a^{18}\,b+96\,C^3\,a^{17}\,b^2-128\,C^3\,a^{16}\,b^3-128\,C^3\,a^{15}\,b^4+220\,C^3\,a^{14}\,b^5+132\,C^3\,a^{13}\,b^6-220\,C^3\,a^{12}\,b^7-68\,C^3\,a^{11}\,b^8+140\,C^3\,a^{10}\,b^9+22\,C^3\,a^9\,b^{10}-52\,C^3\,a^8\,b^{11}-4\,C^3\,a^7\,b^{12}+8\,C^3\,a^6\,b^{13}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)}{a^6}+\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)}{a^6}}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2+10{}\mathrm{i}\,A\,b^2\right)\,2{}\mathrm{i}}{a^6\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2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\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*a^8 + 20*A*b^8 - 59*A*a^2*b^6 - 27*A*a^3*b^5 + 57*A*a^4*b^4 + 21*A*a^5*b^3 - 11*A*a^6*b^2 + 2*C*a^2*b^6 + C*a^3*b^5 - 6*C*a^4*b^4 - 4*C*a^5*b^3 + 12*C*a^6*b^2 + 10*A*a*b^7 - 7*A*a^7*b))/(a^5*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^9*(A*a^8 + 20*A*b^8 - 59*A*a^2*b^6 + 27*A*a^3*b^5 + 57*A*a^4*b^4 - 21*A*a^5*b^3 - 11*A*a^6*b^2 + 2*C*a^2*b^6 - C*a^3*b^5 - 6*C*a^4*b^4 + 4*C*a^5*b^3 + 12*C*a^6*b^2 - 10*A*a*b^7 + 7*A*a^7*b))/(a^5*(a + b)^3*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(120*A*b^9 - 6*A*a^9 - 364*A*a^2*b^7 - 71*A*a^3*b^6 + 369*A*a^4*b^5 + 45*A*a^5*b^4 - 111*A*a^6*b^3 - 3*A*a^7*b^2 + 12*C*a^2*b^7 + 3*C*a^3*b^6 - 37*C*a^4*b^5 - 8*C*a^5*b^4 + 60*C*a^6*b^3 + 30*A*a*b^8 + 21*A*a^8*b))/(3*a^5*(a + b)^2*(a - b)^3) - (2*tan(c/2 + (d*x)/2)^7*(6*A*a^9 + 120*A*b^9 - 364*A*a^2*b^7 + 71*A*a^3*b^6 + 369*A*a^4*b^5 - 45*A*a^5*b^4 - 111*A*a^6*b^3 + 3*A*a^7*b^2 + 12*C*a^2*b^7 - 3*C*a^3*b^6 - 37*C*a^4*b^5 + 8*C*a^5*b^4 + 60*C*a^6*b^3 - 30*A*a*b^8 + 21*A*a^8*b))/(3*a^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(9*A*a^10 + 180*A*b^10 - 611*A*a^2*b^8 + 740*A*a^4*b^6 - 324*A*a^6*b^4 + 36*A*a^8*b^2 + 18*C*a^2*b^8 - 62*C*a^4*b^6 + 110*C*a^6*b^4 - 36*C*a^8*b^2))/(3*a^5*(a + b)^3*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(9*a*b^2 + 3*a^2*b - a^3 + 5*b^3) + tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 2*a^3 + 10*b^3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 2*a^3 - 10*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a^2*b - 9*a*b^2 + a^3 + 5*b^3))) - (atan((((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 + (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*1i)/a^6 - ((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 - (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*1i)/a^6)/(((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 + (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))/a^6 - (8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + ((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(((A*b^2*10i + a^2*((A*1i)/2 + C*1i))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 - (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))/a^6))*(A*b^2*10i + a^2*((A*1i)/2 + C*1i))*2i)/(a^6*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*1i)/(d*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))","B"
705,1,57,17,3.693861,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(2*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
706,1,182,52,3.980154,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^2,x)","x-\frac{4\,b\,\mathrm{atanh}\left(\frac{8\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(a\,\left(a^2-b^2\right)+b\,\left(a^2-b^2\right)+4\,a\,b^2-2\,a^2\,b-2\,b^3\right)}\right)}{d\,\sqrt{a^2-b^2}}","Not used",1,"x - (4*b*atanh((8*b^4*sin(c/2 + (d*x)/2) + a^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a*b^3*sin(c/2 + (d*x)/2) - 2*a*b*sin(c/2 + (d*x)/2)*(a^2 - b^2))/(cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(a*(a^2 - b^2) + b*(a^2 - b^2) + 4*a*b^2 - 2*a^2*b - 2*b^3))))/(d*(a^2 - b^2)^(1/2))","B"
707,1,2739,107,9.470712,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^3,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)\,32{}\mathrm{i}}{a\,\left(-a^3-a^2\,b+a\,b^2+b^3\right)}\right)\,1{}\mathrm{i}}{a}}{a}-\frac{-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)\,32{}\mathrm{i}}{a\,\left(-a^3-a^2\,b+a\,b^2+b^3\right)}\right)\,1{}\mathrm{i}}{a}}{a}}{\frac{64\,\left(3\,a^4\,b+6\,a^3\,b^2-4\,a^2\,b^3-2\,a\,b^4+b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)\,32{}\mathrm{i}}{a\,\left(-a^3-a^2\,b+a\,b^2+b^3\right)}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}+\frac{\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)\,32{}\mathrm{i}}{a\,\left(-a^3-a^2\,b+a\,b^2+b^3\right)}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}}\right)}{a\,d}+\frac{4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{b\,\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)}{\left(-a^3-a^2\,b+a\,b^2+b^3\right)\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}-\frac{b\,\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)}{\left(-a^3-a^2\,b+a\,b^2+b^3\right)\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}}{\frac{64\,\left(3\,a^4\,b+6\,a^3\,b^2-4\,a^2\,b^3-2\,a\,b^4+b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{b\,\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)}{\left(-a^3-a^2\,b+a\,b^2+b^3\right)\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}-\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+8\,a^4\,b^2+4\,a^3\,b^3-7\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{-a^3-a^2\,b+a\,b^2+b^3}-\frac{b\,\left(\frac{32\,\left(-a^7+3\,a^6\,b-4\,a^4\,b^3+a^3\,b^4+a^2\,b^5\right)}{-a^3-a^2\,b+a\,b^2+b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^7\,b-2\,a^6\,b^2-4\,a^5\,b^3+4\,a^4\,b^4+2\,a^3\,b^5-2\,a^2\,b^6\right)}{\left(-a^3-a^2\,b+a\,b^2+b^3\right)\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6\right)}","Not used",1,"(2*atan((((((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) - (tan(c/2 + (d*x)/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2)*32i)/(a*(a*b^2 - a^2*b - a^3 + b^3)))*1i)/a + (32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3))/a - ((((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) + (tan(c/2 + (d*x)/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2)*32i)/(a*(a*b^2 - a^2*b - a^3 + b^3)))*1i)/a - (32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3))/a)/((((((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) - (tan(c/2 + (d*x)/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2)*32i)/(a*(a*b^2 - a^2*b - a^3 + b^3)))*1i)/a + (32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3))*1i)/a + (((((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) + (tan(c/2 + (d*x)/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2)*32i)/(a*(a*b^2 - a^2*b - a^3 + b^3)))*1i)/a - (32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3))*1i)/a + (64*(3*a^4*b - 2*a*b^4 + b^5 - 4*a^2*b^3 + 6*a^3*b^2))/(a*b^2 - a^2*b - a^3 + b^3))))/(a*d) + (b*atan(((b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3) + (b*((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) - (32*b*tan(c/2 + (d*x)/2)*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2))/((a*b^2 - a^2*b - a^3 + b^3)*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*1i)/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3) - (b*((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) + (32*b*tan(c/2 + (d*x)/2)*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2))/((a*b^2 - a^2*b - a^3 + b^3)*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*1i)/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))/((64*(3*a^4*b - 2*a*b^4 + b^5 - 4*a^2*b^3 + 6*a^3*b^2))/(a*b^2 - a^2*b - a^3 + b^3) + (b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3) + (b*((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) - (32*b*tan(c/2 + (d*x)/2)*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2))/((a*b^2 - a^2*b - a^3 + b^3)*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2) - (b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 7*a^2*b^4 + 4*a^3*b^3 + 8*a^4*b^2))/(a*b^2 - a^2*b - a^3 + b^3) - (b*((32*(3*a^6*b - a^7 + a^2*b^5 + a^3*b^4 - 4*a^4*b^3))/(a*b^2 - a^2*b - a^3 + b^3) + (32*b*tan(c/2 + (d*x)/2)*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^7*b - 2*a^2*b^6 + 2*a^3*b^5 + 4*a^4*b^4 - 4*a^5*b^3 - 2*a^6*b^2))/((a*b^2 - a^2*b - a^3 + b^3)*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))*(3*a^2 - b^2)*((a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)) + (4*b^2*tan(c/2 + (d*x)/2))/(d*(a + b)*(a - b)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
708,1,4924,162,12.890688,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^4,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}+\frac{\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)\,32{}\mathrm{i}}{a^2\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,1{}\mathrm{i}}{a^2}}{a^2}-\frac{-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}+\frac{\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)\,32{}\mathrm{i}}{a^2\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,1{}\mathrm{i}}{a^2}}{a^2}}{\frac{64\,\left(4\,a^8\,b+12\,a^7\,b^2-10\,a^6\,b^3-6\,a^5\,b^4+9\,a^4\,b^5+3\,a^3\,b^6-4\,a^2\,b^7+b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}+\frac{\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)\,32{}\mathrm{i}}{a^2\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}+\frac{\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)\,32{}\mathrm{i}}{a^2\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}-\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-5\,a^2\,b^2+a\,b^3+b^4\right)}{\left(a+b\right)\,\left(a^3-2\,a^2\,b+a\,b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a^2\,b^2+a\,b^3-b^4\right)}{{\left(a+b\right)}^2\,\left(a\,b-a^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}+\frac{b\,\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)}{\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}-\frac{b\,\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)}{\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}{\frac{64\,\left(4\,a^8\,b+12\,a^7\,b^2-10\,a^6\,b^3-6\,a^5\,b^4+9\,a^4\,b^5+3\,a^3\,b^6-4\,a^2\,b^7+b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}+\frac{b\,\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)}{\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}-\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+13\,a^8\,b^2+8\,a^7\,b^3-14\,a^6\,b^4-12\,a^5\,b^5+14\,a^4\,b^6+8\,a^3\,b^7-7\,a^2\,b^8-2\,a\,b^9+2\,b^{10}\right)}{a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7}-\frac{b\,\left(\frac{32\,\left(-a^{13}+4\,a^{12}\,b+a^{11}\,b^2-10\,a^{10}\,b^3+9\,a^8\,b^5+a^7\,b^6-4\,a^6\,b^7-a^5\,b^8+a^4\,b^9\right)}{a^{10}+a^9\,b-3\,a^8\,b^2-3\,a^7\,b^3+3\,a^6\,b^4+3\,a^5\,b^5-a^4\,b^6-a^3\,b^7}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,\left(2\,a^{13}\,b-2\,a^{12}\,b^2-8\,a^{11}\,b^3+8\,a^{10}\,b^4+12\,a^9\,b^5-12\,a^8\,b^6-8\,a^7\,b^7+8\,a^6\,b^8+2\,a^5\,b^9-2\,a^4\,b^{10}\right)}{\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)\,\left(a^9+a^8\,b-3\,a^7\,b^2-3\,a^6\,b^3+3\,a^5\,b^4+3\,a^4\,b^5-a^3\,b^6-a^2\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-2\,a^2\,b^2+b^4\right)\,2{}\mathrm{i}}{d\,\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)}","Not used",1,"(2*atan((((((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) - (tan(c/2 + (d*x)/2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2)*32i)/(a^2*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*1i)/a^2 + (32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2))/a^2 - ((((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) + (tan(c/2 + (d*x)/2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2)*32i)/(a^2*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*1i)/a^2 - (32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2))/a^2)/((64*(4*a^8*b + b^9 - 4*a^2*b^7 + 3*a^3*b^6 + 9*a^4*b^5 - 6*a^5*b^4 - 10*a^6*b^3 + 12*a^7*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) + (((((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) - (tan(c/2 + (d*x)/2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2)*32i)/(a^2*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*1i)/a^2 + (32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2))*1i)/a^2 + (((((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) + (tan(c/2 + (d*x)/2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2)*32i)/(a^2*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*1i)/a^2 - (32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2))*1i)/a^2)))/(a^2*d) - ((2*tan(c/2 + (d*x)/2)*(a*b^3 + b^4 - 5*a^2*b^2))/((a + b)*(a*b^2 - 2*a^2*b + a^3)) - (2*tan(c/2 + (d*x)/2)^3*(a*b^3 - b^4 + 5*a^2*b^2))/((a + b)^2*(a*b - a^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (b*atan(((b*((32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2) + (b*((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2))/((a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2) - (b*((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2))/((a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))/((64*(4*a^8*b + b^9 - 4*a^2*b^7 + 3*a^3*b^6 + 9*a^4*b^5 - 6*a^5*b^4 - 10*a^6*b^3 + 12*a^7*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2) + (b*((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2))/((a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) - (b*((32*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 2*a*b^9 + 2*b^10 - 7*a^2*b^8 + 8*a^3*b^7 + 14*a^4*b^6 - 12*a^5*b^5 - 14*a^6*b^4 + 8*a^7*b^3 + 13*a^8*b^2))/(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2) - (b*((32*(4*a^12*b - a^13 + a^4*b^9 - a^5*b^8 - 4*a^6*b^7 + a^7*b^6 + 9*a^8*b^5 - 10*a^10*b^3 + a^11*b^2))/(a^9*b + a^10 - a^3*b^7 - a^4*b^6 + 3*a^5*b^5 + 3*a^6*b^4 - 3*a^7*b^3 - 3*a^8*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*(2*a^13*b - 2*a^4*b^10 + 2*a^5*b^9 + 8*a^6*b^8 - 8*a^7*b^7 - 12*a^8*b^6 + 12*a^9*b^5 + 8*a^10*b^4 - 8*a^11*b^3 - 2*a^12*b^2))/((a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)*(a^8*b + a^9 - a^2*b^7 - a^3*b^6 + 3*a^4*b^5 + 3*a^5*b^4 - 3*a^6*b^3 - 3*a^7*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + b^4 - 2*a^2*b^2)*2i)/(d*(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))","B"
709,0,-1,467,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
710,0,-1,375,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
711,0,-1,308,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
712,0,-1,355,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
713,0,-1,352,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
714,0,-1,411,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
715,0,-1,502,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
716,0,-1,587,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
717,0,-1,550,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
718,0,-1,454,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
719,0,-1,374,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
720,0,-1,415,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
721,0,-1,408,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
722,0,-1,414,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
723,0,-1,504,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
724,0,-1,583,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
725,0,-1,650,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
726,0,-1,534,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
727,0,-1,454,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
728,0,-1,481,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
729,0,-1,478,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
730,0,-1,463,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
731,0,-1,507,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
732,0,-1,587,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
733,0,-1,403,0.000000,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","-\int -\left(a^2-\frac{b^2}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"-int(-(a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
734,0,-1,353,0.000000,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","-\int -\left(a^2-\frac{b^2}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"-int(-(a^2 - b^2/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
735,0,-1,393,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)), x)","F"
736,0,-1,320,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)), x)","F"
737,0,-1,253,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)), x)","F"
738,0,-1,313,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2), x)","F"
739,0,-1,352,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
740,0,-1,411,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
741,0,-1,506,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
742,0,-1,460,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)), x)","F"
743,0,-1,327,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)), x)","F"
744,0,-1,279,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)), x)","F"
745,0,-1,381,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2), x)","F"
746,0,-1,431,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
747,0,-1,501,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
748,0,-1,488,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)), x)","F"
749,0,-1,408,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)), x)","F"
750,0,-1,378,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)), x)","F"
751,0,-1,517,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2), x)","F"
752,0,-1,559,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
753,0,-1,645,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
754,0,-1,626,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(7/2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(7/2), x)","F"
755,0,-1,303,0.000000,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2),x)","-\int -\frac{a^2-\frac{b^2}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"-int(-(a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2), x)","F"
756,0,-1,200,0.000000,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2),x)","-\int -\frac{a^2-\frac{b^2}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"-int(-(a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2), x)","F"
757,0,-1,338,0.000000,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2),x)","-\int -\frac{a^2-\frac{b^2}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"-int(-(a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2), x)","F"
758,0,-1,445,0.000000,"\text{Not used}","int((a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(7/2),x)","-\int -\frac{a^2-\frac{b^2}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"-int(-(a^2 - b^2/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(7/2), x)","F"
759,0,-1,145,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
760,0,-1,213,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
761,0,-1,243,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(2/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",0,"int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(2/3), x)","F"
762,0,-1,243,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/3),x)","\int \left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",0,"int((A + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/3), x)","F"
763,0,-1,240,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/3), x)","F"
764,0,-1,240,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int((A + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(2/3), x)","F"
765,1,234,145,7.947302,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,B\,b}{4}+\frac{3\,C\,a}{4}\right)}{d}-\frac{\left(2\,B\,a-\frac{5\,B\,b}{4}-\frac{5\,C\,a}{4}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B\,b}{2}-\frac{16\,B\,a}{3}+\frac{C\,a}{2}-\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,B\,a}{3}+\frac{116\,C\,b}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,B\,a}{3}-\frac{B\,b}{2}-\frac{C\,a}{2}-\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a+\frac{5\,B\,b}{4}+\frac{5\,C\,a}{4}+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((3*B*b)/4 + (3*C*a)/4))/d - (tan(c/2 + (d*x)/2)*(2*B*a + (5*B*b)/4 + (5*C*a)/4 + 2*C*b) + tan(c/2 + (d*x)/2)^5*((20*B*a)/3 + (116*C*b)/15) + tan(c/2 + (d*x)/2)^9*(2*B*a - (5*B*b)/4 - (5*C*a)/4 + 2*C*b) - tan(c/2 + (d*x)/2)^3*((16*B*a)/3 + (B*b)/2 + (C*a)/2 + (8*C*b)/3) - tan(c/2 + (d*x)/2)^7*((16*B*a)/3 - (B*b)/2 - (C*a)/2 + (8*C*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
766,1,194,114,7.702416,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{\left(B\,a-2\,B\,b-2\,C\,a+\frac{5\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{10\,B\,b}{3}-B\,a+\frac{10\,C\,a}{3}+\frac{3\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,C\,b}{4}-\frac{10\,B\,b}{3}-\frac{10\,C\,a}{3}-B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B\,a+2\,B\,b+2\,C\,a+\frac{5\,C\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B\,a+\frac{3\,C\,b}{4}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(B*a + 2*B*b + 2*C*a + (5*C*b)/4) + tan(c/2 + (d*x)/2)^7*(B*a - 2*B*b - 2*C*a + (5*C*b)/4) - tan(c/2 + (d*x)/2)^3*(B*a + (10*B*b)/3 + (10*C*a)/3 - (3*C*b)/4) + tan(c/2 + (d*x)/2)^5*((10*B*b)/3 - B*a + (10*C*a)/3 + (3*C*b)/4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh(tan(c/2 + (d*x)/2))*(B*a + (3*C*b)/4))/d","B"
767,1,145,93,6.187983,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)))/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B\,b+C\,a\right)}{d}-\frac{\left(2\,B\,a-B\,b-C\,a+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,B\,a-\frac{4\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a+B\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(B*b + C*a))/d - (tan(c/2 + (d*x)/2)*(2*B*a + B*b + C*a + 2*C*b) - tan(c/2 + (d*x)/2)^3*(4*B*a + (4*C*b)/3) + tan(c/2 + (d*x)/2)^5*(2*B*a - B*b - C*a + 2*C*b))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
768,1,104,61,4.772902,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b+2\,C\,a+C\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b+2\,C\,a-C\,b\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,B\,a+C\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*B*b + 2*C*a + C*b) - tan(c/2 + (d*x)/2)^3*(2*B*b + 2*C*a - C*b))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (atanh(tan(c/2 + (d*x)/2))*(2*B*a + C*b))/d","B"
769,1,114,35,3.867364,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (B*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (C*b*sin(c + d*x))/(d*cos(c + d*x))","B"
770,1,100,35,3.793178,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(B*a*sin(c + d*x))/d + (2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
771,1,50,52,3.649341,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{B\,a\,x}{2}+C\,b\,x+\frac{B\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(B*a*x)/2 + C*b*x + (B*b*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (B*a*sin(2*c + 2*d*x))/(4*d)","B"
772,1,84,84,3.955602,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{B\,b\,x}{2}+\frac{C\,a\,x}{2}+\frac{3\,B\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(B*b*x)/2 + (C*a*x)/2 + (3*B*a*sin(c + d*x))/(4*d) + (C*b*sin(c + d*x))/d + (B*a*sin(3*c + 3*d*x))/(12*d) + (B*b*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d)","B"
773,1,117,105,3.810544,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{3\,B\,a\,x}{8}+\frac{C\,b\,x}{2}+\frac{3\,B\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{B\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(3*B*a*x)/8 + (C*b*x)/2 + (3*B*b*sin(c + d*x))/(4*d) + (3*C*a*sin(c + d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d) + (B*a*sin(4*c + 4*d*x))/(32*d) + (B*b*sin(3*c + 3*d*x))/(12*d) + (C*a*sin(3*c + 3*d*x))/(12*d) + (C*b*sin(2*c + 2*d*x))/(4*d)","B"
774,1,149,136,3.972793,"\text{Not used}","int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x)),x)","\frac{3\,B\,b\,x}{8}+\frac{3\,C\,a\,x}{8}+\frac{5\,B\,a\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,C\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,B\,a\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,a\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(3*B*b*x)/8 + (3*C*a*x)/8 + (5*B*a*sin(c + d*x))/(8*d) + (3*C*b*sin(c + d*x))/(4*d) + (5*B*a*sin(3*c + 3*d*x))/(48*d) + (B*a*sin(5*c + 5*d*x))/(80*d) + (B*b*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (B*b*sin(4*c + 4*d*x))/(32*d) + (C*a*sin(4*c + 4*d*x))/(32*d) + (C*b*sin(3*c + 3*d*x))/(12*d)","B"
775,1,359,198,7.681808,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,a^2}{2}+\frac{3\,C\,a\,b}{4}+\frac{3\,B\,b^2}{8}\right)}{2\,B\,a^2+3\,C\,a\,b+\frac{3\,B\,b^2}{2}}\right)\,\left(B\,a^2+\frac{3\,C\,a\,b}{2}+\frac{3\,B\,b^2}{4}\right)}{d}-\frac{\left(2\,C\,a^2-\frac{5\,B\,b^2}{4}-B\,a^2+2\,C\,b^2+4\,B\,a\,b-\frac{5\,C\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,B\,a^2+\frac{B\,b^2}{2}-\frac{16\,C\,a^2}{3}-\frac{8\,C\,b^2}{3}-\frac{32\,B\,a\,b}{3}+C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,C\,a^2}{3}+\frac{40\,B\,a\,b}{3}+\frac{116\,C\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-2\,B\,a^2-\frac{B\,b^2}{2}-\frac{16\,C\,a^2}{3}-\frac{8\,C\,b^2}{3}-\frac{32\,B\,a\,b}{3}-C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B\,a^2+\frac{5\,B\,b^2}{4}+2\,C\,a^2+2\,C\,b^2+4\,B\,a\,b+\frac{5\,C\,a\,b}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((B*a^2)/2 + (3*B*b^2)/8 + (3*C*a*b)/4))/(2*B*a^2 + (3*B*b^2)/2 + 3*C*a*b))*(B*a^2 + (3*B*b^2)/4 + (3*C*a*b)/2))/d - (tan(c/2 + (d*x)/2)^5*((20*C*a^2)/3 + (116*C*b^2)/15 + (40*B*a*b)/3) - tan(c/2 + (d*x)/2)^9*(B*a^2 + (5*B*b^2)/4 - 2*C*a^2 - 2*C*b^2 - 4*B*a*b + (5*C*a*b)/2) - tan(c/2 + (d*x)/2)^3*(2*B*a^2 + (B*b^2)/2 + (16*C*a^2)/3 + (8*C*b^2)/3 + (32*B*a*b)/3 + C*a*b) + tan(c/2 + (d*x)/2)^7*(2*B*a^2 + (B*b^2)/2 - (16*C*a^2)/3 - (8*C*b^2)/3 - (32*B*a*b)/3 + C*a*b) + tan(c/2 + (d*x)/2)*(B*a^2 + (5*B*b^2)/4 + 2*C*a^2 + 2*C*b^2 + 4*B*a*b + (5*C*a*b)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
776,1,317,179,7.686855,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2)/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{C\,a^2}{2}+B\,a\,b+\frac{3\,C\,b^2}{8}\right)}{2\,C\,a^2+4\,B\,a\,b+\frac{3\,C\,b^2}{2}}\right)\,\left(C\,a^2+2\,B\,a\,b+\frac{3\,C\,b^2}{4}\right)}{d}-\frac{\left(2\,B\,a^2+2\,B\,b^2-C\,a^2-\frac{5\,C\,b^2}{4}-2\,B\,a\,b+4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(C\,a^2-\frac{10\,B\,b^2}{3}-6\,B\,a^2-\frac{3\,C\,b^2}{4}+2\,B\,a\,b-\frac{20\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,B\,a^2+\frac{10\,B\,b^2}{3}+C\,a^2-\frac{3\,C\,b^2}{4}+2\,B\,a\,b+\frac{20\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,B\,a^2-2\,B\,b^2-C\,a^2-\frac{5\,C\,b^2}{4}-2\,B\,a\,b-4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((C*a^2)/2 + (3*C*b^2)/8 + B*a*b))/(2*C*a^2 + (3*C*b^2)/2 + 4*B*a*b))*(C*a^2 + (3*C*b^2)/4 + 2*B*a*b))/d - (tan(c/2 + (d*x)/2)^7*(2*B*a^2 + 2*B*b^2 - C*a^2 - (5*C*b^2)/4 - 2*B*a*b + 4*C*a*b) + tan(c/2 + (d*x)/2)^3*(6*B*a^2 + (10*B*b^2)/3 + C*a^2 - (3*C*b^2)/4 + 2*B*a*b + (20*C*a*b)/3) - tan(c/2 + (d*x)/2)^5*(6*B*a^2 + (10*B*b^2)/3 - C*a^2 + (3*C*b^2)/4 - 2*B*a*b + (20*C*a*b)/3) - tan(c/2 + (d*x)/2)*(2*B*a^2 + 2*B*b^2 + C*a^2 + (5*C*b^2)/4 + 2*B*a*b + 4*C*a*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
777,1,227,116,7.380863,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a^2+C\,a\,b+\frac{B\,b^2}{2}\right)}{4\,B\,a^2+4\,C\,a\,b+2\,B\,b^2}\right)\,\left(2\,B\,a^2+2\,C\,a\,b+B\,b^2\right)}{d}-\frac{\left(2\,C\,a^2-B\,b^2+2\,C\,b^2+4\,B\,a\,b-2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,C\,a^2-8\,B\,a\,b-\frac{4\,C\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B\,b^2+2\,C\,a^2+2\,C\,b^2+4\,B\,a\,b+2\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*(B*a^2 + (B*b^2)/2 + C*a*b))/(4*B*a^2 + 2*B*b^2 + 4*C*a*b))*(2*B*a^2 + B*b^2 + 2*C*a*b))/d - (tan(c/2 + (d*x)/2)*(B*b^2 + 2*C*a^2 + 2*C*b^2 + 4*B*a*b + 2*C*a*b) - tan(c/2 + (d*x)/2)^3*(4*C*a^2 + (4*C*b^2)/3 + 8*B*a*b) + tan(c/2 + (d*x)/2)^5*(2*C*a^2 - B*b^2 + 2*C*b^2 + 4*B*a*b - 2*C*a*b))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
778,1,176,86,4.476817,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{2\,\left(B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+2\,B\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{2}+C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 2*B*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((B*b^2*sin(2*c + 2*d*x))/2 + (C*b^2*sin(c + d*x))/2 + C*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
779,1,163,60,4.276515,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{C\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}+\frac{4\,B\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(C*b^2*tan(c + d*x))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^2*sin(2*c + 2*d*x))/(2*d*cos(c + d*x)) + (4*B*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
780,1,169,80,3.990155,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,B\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(C*a^2*sin(c + d*x))/d + (B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^2*sin(2*c + 2*d*x))/(4*d) + (2*B*a*b*sin(c + d*x))/d + (4*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
781,1,115,107,3.731056,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{C\,a^2\,x}{2}+C\,b^2\,x+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b^2\,\sin\left(c+d\,x\right)}{d}+B\,a\,b\,x+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,C\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(C*a^2*x)/2 + C*b^2*x + (3*B*a^2*sin(c + d*x))/(4*d) + (B*b^2*sin(c + d*x))/d + B*a*b*x + (B*a^2*sin(3*c + 3*d*x))/(12*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (2*C*a*b*sin(c + d*x))/d + (B*a*b*sin(2*c + 2*d*x))/(2*d)","B"
782,1,169,136,3.782538,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{3\,B\,a^2\,x}{8}+\frac{B\,b^2\,x}{2}+\frac{3\,C\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{d}+C\,a\,b\,x+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,B\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{B\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(3*B*a^2*x)/8 + (B*b^2*x)/2 + (3*C*a^2*sin(c + d*x))/(4*d) + (C*b^2*sin(c + d*x))/d + C*a*b*x + (B*a^2*sin(2*c + 2*d*x))/(4*d) + (B*a^2*sin(4*c + 4*d*x))/(32*d) + (B*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(3*c + 3*d*x))/(12*d) + (3*B*a*b*sin(c + d*x))/(2*d) + (B*a*b*sin(3*c + 3*d*x))/(6*d) + (C*a*b*sin(2*c + 2*d*x))/(2*d)","B"
783,1,307,180,7.632536,"\text{Not used}","int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^2,x)","\frac{x\,\left(\frac{3\,C\,a^2}{4}+\frac{3\,B\,a\,b}{2}+C\,b^2\right)}{2}+\frac{\left(2\,B\,a^2+2\,B\,b^2-\frac{5\,C\,a^2}{4}-C\,b^2-\frac{5\,B\,a\,b}{2}+4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,B\,a^2}{3}+\frac{16\,B\,b^2}{3}-\frac{C\,a^2}{2}-2\,C\,b^2-B\,a\,b+\frac{32\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,B\,a^2}{15}+\frac{40\,C\,a\,b}{3}+\frac{20\,B\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,B\,a^2}{3}+\frac{16\,B\,b^2}{3}+\frac{C\,a^2}{2}+2\,C\,b^2+B\,a\,b+\frac{32\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a^2+2\,B\,b^2+\frac{5\,C\,a^2}{4}+C\,b^2+\frac{5\,B\,a\,b}{2}+4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*((3*C*a^2)/4 + C*b^2 + (3*B*a*b)/2))/2 + (tan(c/2 + (d*x)/2)^5*((116*B*a^2)/15 + (20*B*b^2)/3 + (40*C*a*b)/3) + tan(c/2 + (d*x)/2)^9*(2*B*a^2 + 2*B*b^2 - (5*C*a^2)/4 - C*b^2 - (5*B*a*b)/2 + 4*C*a*b) + tan(c/2 + (d*x)/2)^3*((8*B*a^2)/3 + (16*B*b^2)/3 + (C*a^2)/2 + 2*C*b^2 + B*a*b + (32*C*a*b)/3) + tan(c/2 + (d*x)/2)^7*((8*B*a^2)/3 + (16*B*b^2)/3 - (C*a^2)/2 - 2*C*b^2 - B*a*b + (32*C*a*b)/3) + tan(c/2 + (d*x)/2)*(2*B*a^2 + 2*B*b^2 + (5*C*a^2)/4 + C*b^2 + (5*B*a*b)/2 + 4*C*a*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1))","B"
784,1,571,278,7.542368,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,a^3}{2}+\frac{9\,C\,a^2\,b}{8}+\frac{9\,B\,a\,b^2}{8}+\frac{5\,C\,b^3}{16}\right)}{2\,B\,a^3+\frac{9\,C\,a^2\,b}{2}+\frac{9\,B\,a\,b^2}{2}+\frac{5\,C\,b^3}{4}}\right)\,\left(B\,a^3+\frac{9\,C\,a^2\,b}{4}+\frac{9\,B\,a\,b^2}{4}+\frac{5\,C\,b^3}{8}\right)}{d}+\frac{\left(B\,a^3-2\,B\,b^3-2\,C\,a^3+\frac{11\,C\,b^3}{8}+\frac{15\,B\,a\,b^2}{4}-6\,B\,a^2\,b-6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{14\,B\,b^3}{3}-3\,B\,a^3+\frac{22\,C\,a^3}{3}+\frac{5\,C\,b^3}{24}-\frac{21\,B\,a\,b^2}{4}+22\,B\,a^2\,b+14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,B\,a^3-\frac{52\,B\,b^3}{5}-12\,C\,a^3+\frac{15\,C\,b^3}{4}+\frac{3\,B\,a\,b^2}{2}-36\,B\,a^2\,b-\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(2\,B\,a^3+\frac{52\,B\,b^3}{5}+12\,C\,a^3+\frac{15\,C\,b^3}{4}+\frac{3\,B\,a\,b^2}{2}+36\,B\,a^2\,b+\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,C\,b^3}{24}-\frac{14\,B\,b^3}{3}-\frac{22\,C\,a^3}{3}-3\,B\,a^3-\frac{21\,B\,a\,b^2}{4}-22\,B\,a^2\,b-14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B\,a^3+2\,B\,b^3+2\,C\,a^3+\frac{11\,C\,b^3}{8}+\frac{15\,B\,a\,b^2}{4}+6\,B\,a^2\,b+6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((B*a^3)/2 + (5*C*b^3)/16 + (9*B*a*b^2)/8 + (9*C*a^2*b)/8))/(2*B*a^3 + (5*C*b^3)/4 + (9*B*a*b^2)/2 + (9*C*a^2*b)/2))*(B*a^3 + (5*C*b^3)/8 + (9*B*a*b^2)/4 + (9*C*a^2*b)/4))/d + (tan(c/2 + (d*x)/2)*(B*a^3 + 2*B*b^3 + 2*C*a^3 + (11*C*b^3)/8 + (15*B*a*b^2)/4 + 6*B*a^2*b + 6*C*a*b^2 + (15*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^11*(B*a^3 - 2*B*b^3 - 2*C*a^3 + (11*C*b^3)/8 + (15*B*a*b^2)/4 - 6*B*a^2*b - 6*C*a*b^2 + (15*C*a^2*b)/4) - tan(c/2 + (d*x)/2)^3*(3*B*a^3 + (14*B*b^3)/3 + (22*C*a^3)/3 - (5*C*b^3)/24 + (21*B*a*b^2)/4 + 22*B*a^2*b + 14*C*a*b^2 + (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^9*((14*B*b^3)/3 - 3*B*a^3 + (22*C*a^3)/3 + (5*C*b^3)/24 - (21*B*a*b^2)/4 + 22*B*a^2*b + 14*C*a*b^2 - (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^5*(2*B*a^3 + (52*B*b^3)/5 + 12*C*a^3 + (15*C*b^3)/4 + (3*B*a*b^2)/2 + 36*B*a^2*b + (156*C*a*b^2)/5 + (3*C*a^2*b)/2) + tan(c/2 + (d*x)/2)^7*(2*B*a^3 - (52*B*b^3)/5 - 12*C*a^3 + (15*C*b^3)/4 + (3*B*a*b^2)/2 - 36*B*a^2*b - (156*C*a*b^2)/5 + (3*C*a^2*b)/2))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
785,1,470,252,7.733583,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3)/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{C\,a^3}{2}+\frac{3\,B\,a^2\,b}{2}+\frac{9\,C\,a\,b^2}{8}+\frac{3\,B\,b^3}{8}\right)}{2\,C\,a^3+6\,B\,a^2\,b+\frac{9\,C\,a\,b^2}{2}+\frac{3\,B\,b^3}{2}}\right)\,\left(C\,a^3+3\,B\,a^2\,b+\frac{9\,C\,a\,b^2}{4}+\frac{3\,B\,b^3}{4}\right)}{d}-\frac{\left(2\,B\,a^3-\frac{5\,B\,b^3}{4}-C\,a^3+2\,C\,b^3+6\,B\,a\,b^2-3\,B\,a^2\,b-\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B\,b^3}{2}-8\,B\,a^3+2\,C\,a^3-\frac{8\,C\,b^3}{3}-16\,B\,a\,b^2+6\,B\,a^2\,b+\frac{3\,C\,a\,b^2}{2}-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,B\,a^3+20\,C\,a^2\,b+20\,B\,a\,b^2+\frac{116\,C\,b^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,B\,a^3-\frac{B\,b^3}{2}-2\,C\,a^3-\frac{8\,C\,b^3}{3}-16\,B\,a\,b^2-6\,B\,a^2\,b-\frac{3\,C\,a\,b^2}{2}-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a^3+\frac{5\,B\,b^3}{4}+C\,a^3+2\,C\,b^3+6\,B\,a\,b^2+3\,B\,a^2\,b+\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*B*b^3)/8 + (C*a^3)/2 + (3*B*a^2*b)/2 + (9*C*a*b^2)/8))/((3*B*b^3)/2 + 2*C*a^3 + 6*B*a^2*b + (9*C*a*b^2)/2))*((3*B*b^3)/4 + C*a^3 + 3*B*a^2*b + (9*C*a*b^2)/4))/d - (tan(c/2 + (d*x)/2)*(2*B*a^3 + (5*B*b^3)/4 + C*a^3 + 2*C*b^3 + 6*B*a*b^2 + 3*B*a^2*b + (15*C*a*b^2)/4 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^5*(12*B*a^3 + (116*C*b^3)/15 + 20*B*a*b^2 + 20*C*a^2*b) + tan(c/2 + (d*x)/2)^9*(2*B*a^3 - (5*B*b^3)/4 - C*a^3 + 2*C*b^3 + 6*B*a*b^2 - 3*B*a^2*b - (15*C*a*b^2)/4 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*(8*B*a^3 + (B*b^3)/2 + 2*C*a^3 + (8*C*b^3)/3 + 16*B*a*b^2 + 6*B*a^2*b + (3*C*a*b^2)/2 + 16*C*a^2*b) - tan(c/2 + (d*x)/2)^7*(8*B*a^3 - (B*b^3)/2 - 2*C*a^3 + (8*C*b^3)/3 + 16*B*a*b^2 - 6*B*a^2*b - (3*C*a*b^2)/2 + 16*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
786,1,395,180,7.780468,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a^3+\frac{3\,C\,a^2\,b}{2}+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,b^3}{8}\right)}{4\,B\,a^3+6\,C\,a^2\,b+6\,B\,a\,b^2+\frac{3\,C\,b^3}{2}}\right)\,\left(2\,B\,a^3+3\,C\,a^2\,b+3\,B\,a\,b^2+\frac{3\,C\,b^3}{4}\right)}{d}-\frac{\left(2\,B\,b^3+2\,C\,a^3-\frac{5\,C\,b^3}{4}-3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(3\,B\,a\,b^2-6\,C\,a^3-\frac{3\,C\,b^3}{4}-\frac{10\,B\,b^3}{3}-18\,B\,a^2\,b-10\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{10\,B\,b^3}{3}+6\,C\,a^3-\frac{3\,C\,b^3}{4}+3\,B\,a\,b^2+18\,B\,a^2\,b+10\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,B\,b^3-2\,C\,a^3-\frac{5\,C\,b^3}{4}-3\,B\,a\,b^2-6\,B\,a^2\,b-6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*(B*a^3 + (3*C*b^3)/8 + (3*B*a*b^2)/2 + (3*C*a^2*b)/2))/(4*B*a^3 + (3*C*b^3)/2 + 6*B*a*b^2 + 6*C*a^2*b))*(2*B*a^3 + (3*C*b^3)/4 + 3*B*a*b^2 + 3*C*a^2*b))/d - (tan(c/2 + (d*x)/2)^7*(2*B*b^3 + 2*C*a^3 - (5*C*b^3)/4 - 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b) + tan(c/2 + (d*x)/2)^3*((10*B*b^3)/3 + 6*C*a^3 - (3*C*b^3)/4 + 3*B*a*b^2 + 18*B*a^2*b + 10*C*a*b^2 + 3*C*a^2*b) - tan(c/2 + (d*x)/2)^5*((10*B*b^3)/3 + 6*C*a^3 + (3*C*b^3)/4 - 3*B*a*b^2 + 18*B*a^2*b + 10*C*a*b^2 - 3*C*a^2*b) - tan(c/2 + (d*x)/2)*(2*B*b^3 + 2*C*a^3 + (5*C*b^3)/4 + 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
787,1,526,137,5.578026,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4}+\frac{3\,B\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{B\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4}-\frac{C\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}+\frac{3\,B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{4}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}-\frac{B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{2}-\frac{C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{4}-\frac{B\,a^2\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{2}-\frac{C\,a\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{4}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((B*b^3*sin(2*c + 2*d*x))/4 + (C*b^3*sin(3*c + 3*d*x))/6 + (C*b^3*sin(c + d*x))/2 + (3*B*a*b^2*sin(c + d*x))/4 + (3*C*a^2*b*sin(c + d*x))/4 + (3*B*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (B*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 - (C*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 + (3*B*a*b^2*sin(3*c + 3*d*x))/4 + (3*C*a*b^2*sin(2*c + 2*d*x))/4 + (3*C*a^2*b*sin(3*c + 3*d*x))/4 + (B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (B*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/4 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 - (B*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/2 - (C*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/4 - (B*a^2*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2 - (C*a*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/4)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
788,1,249,131,5.065577,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(-C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2}-3\,B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}+C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}\right)}{d}","Not used",1,"((B*a^3*sin(3*c + 3*d*x))/4 + (B*b^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(c + d*x))/4 + (C*b^3*sin(c + d*x))/2 + (3*C*a*b^2*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*((C*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2 - C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 3*B*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i + C*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i))/d","B"
789,1,236,124,4.757134,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}+6\,B\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+6\,C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}+\frac{\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{8}+C\,b^3\,\sin\left(c+d\,x\right)+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 6*B*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*C*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - C*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/d + ((B*a^3*sin(3*c + 3*d*x))/8 + (C*a^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(c + d*x))/8 + C*b^3*sin(c + d*x) + (3*B*a^2*b*sin(2*c + 2*d*x))/2)/(d*cos(c + d*x))","B"
790,1,1924,145,5.420107,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{\left(2\,B\,a^3-C\,a^3+6\,B\,a\,b^2-3\,B\,a^2\,b+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{4\,B\,a^3}{3}+12\,C\,a^2\,b+12\,B\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a^3+C\,a^3+6\,B\,a\,b^2+3\,B\,a^2\,b+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)\,1{}\mathrm{i}-\left(\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)\,1{}\mathrm{i}}{\left(\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)+\left(\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,C\,a^3}{2}+\frac{3{}\mathrm{i}\,B\,a^2\,b}{2}+3{}\mathrm{i}\,C\,a\,b^2+1{}\mathrm{i}\,B\,b^3\right)-64\,B\,C^2\,b^9+64\,B^2\,C\,b^9-192\,C^3\,a\,b^8+576\,C^3\,a^2\,b^7-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3+384\,B\,C^2\,a\,b^8-96\,B\,C^2\,a^2\,b^7+640\,B\,C^2\,a^3\,b^6+96\,B\,C^2\,a^5\,b^4+192\,B^2\,C\,a^2\,b^7+144\,B^2\,C\,a^4\,b^5}\right)\,\left(C\,a^3+3\,B\,a^2\,b+6\,C\,a\,b^2+2\,B\,b^3\right)}{d}-\frac{C\,b^3\,\mathrm{atan}\left(\frac{C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}}{64\,B^2\,C\,b^9-64\,B\,C^2\,b^9-192\,C^3\,a\,b^8+576\,C^3\,a^2\,b^7-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)-C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)+384\,B\,C^2\,a\,b^8-96\,B\,C^2\,a^2\,b^7+640\,B\,C^2\,a^3\,b^6+96\,B\,C^2\,a^5\,b^4+192\,B^2\,C\,a^2\,b^7+144\,B^2\,C\,a^4\,b^5}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(2*B*a^3 - C*a^3 + 6*B*a*b^2 - 3*B*a^2*b + 6*C*a^2*b) + tan(c/2 + (d*x)/2)*(2*B*a^3 + C*a^3 + 6*B*a*b^2 + 3*B*a^2*b + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*((4*B*a^3)/3 + 12*B*a*b^2 + 12*C*a^2*b))/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) + (atan((((B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2) + tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3))*(B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*1i - ((B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2) - tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3))*(B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*1i)/(((B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2) + tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3))*(B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i) + ((B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2) - tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3))*(B*b^3*1i + (C*a^3*1i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i) - 64*B*C^2*b^9 + 64*B^2*C*b^9 - 192*C^3*a*b^8 + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 + 384*B*C^2*a*b^8 - 96*B*C^2*a^2*b^7 + 640*B*C^2*a^3*b^6 + 96*B*C^2*a^5*b^4 + 192*B^2*C*a^2*b^7 + 144*B^2*C*a^4*b^5))*(2*B*b^3 + C*a^3 + 3*B*a^2*b + 6*C*a*b^2))/d - (C*b^3*atan((C*b^3*(tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3) + C*b^3*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2))*1i + C*b^3*(tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3) - C*b^3*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2))*1i)/(64*B^2*C*b^9 - 64*B*C^2*b^9 - 192*C^3*a*b^8 + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 + C*b^3*(tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3) + C*b^3*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2)) - C*b^3*(tan(c/2 + (d*x)/2)*(32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 192*B*C*a*b^5 + 48*B*C*a^5*b + 320*B*C*a^3*b^3) - C*b^3*(32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*B*a^2*b + 96*C*a*b^2)) + 384*B*C^2*a*b^8 - 96*B*C^2*a^2*b^7 + 640*B*C^2*a^3*b^6 + 96*B*C^2*a^5*b^4 + 192*B^2*C*a^2*b^7 + 144*B^2*C*a^4*b^5))*2i)/d","B"
791,1,202,179,3.862962,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{3\,B\,a^3\,x}{8}+C\,b^3\,x+\frac{3\,B\,a\,b^2\,x}{2}+\frac{3\,C\,a^2\,b\,x}{2}+\frac{B\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,B\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,C\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{9\,B\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*B*a^3*x)/8 + C*b^3*x + (3*B*a*b^2*x)/2 + (3*C*a^2*b*x)/2 + (B*b^3*sin(c + d*x))/d + (3*C*a^3*sin(c + d*x))/(4*d) + (B*a^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(4*c + 4*d*x))/(32*d) + (C*a^3*sin(3*c + 3*d*x))/(12*d) + (3*B*a*b^2*sin(2*c + 2*d*x))/(4*d) + (B*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*C*a^2*b*sin(2*c + 2*d*x))/(4*d) + (9*B*a^2*b*sin(c + d*x))/(4*d) + (3*C*a*b^2*sin(c + d*x))/d","B"
792,1,277,221,4.123031,"\text{Not used}","int(cos(c + d*x)^6*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^3,x)","\frac{B\,b^3\,x}{2}+\frac{3\,C\,a^3\,x}{8}+\frac{9\,B\,a^2\,b\,x}{8}+\frac{3\,C\,a\,b^2\,x}{2}+\frac{5\,B\,a^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,a^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{9\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{9\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(B*b^3*x)/2 + (3*C*a^3*x)/8 + (9*B*a^2*b*x)/8 + (3*C*a*b^2*x)/2 + (5*B*a^3*sin(c + d*x))/(8*d) + (C*b^3*sin(c + d*x))/d + (5*B*a^3*sin(3*c + 3*d*x))/(48*d) + (B*a^3*sin(5*c + 5*d*x))/(80*d) + (B*b^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(4*c + 4*d*x))/(32*d) + (3*B*a^2*b*sin(2*c + 2*d*x))/(4*d) + (B*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*B*a^2*b*sin(4*c + 4*d*x))/(32*d) + (3*C*a*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*b*sin(3*c + 3*d*x))/(4*d) + (9*B*a*b^2*sin(c + d*x))/(4*d) + (9*C*a^2*b*sin(c + d*x))/(4*d)","B"
793,1,4667,187,8.995823,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2+2\,C\,a^2+2\,C\,b^2-2\,B\,a\,b-C\,a\,b\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,a^2-B\,b^2+2\,C\,b^2-2\,B\,a\,b+C\,a\,b\right)}{b^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,C\,a^2-3\,B\,a\,b+C\,b^2\right)}{3\,b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{b^{10}}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{2\,b^4}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{b^{10}}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{2\,b^4}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{b^{10}}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{2\,b^4}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{b^{10}}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{2\,b^4}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{2\,b^4}}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{b^4\,d}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}+\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}-\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(B*b^2 + 2*C*a^2 + 2*C*b^2 - 2*B*a*b - C*a*b))/b^3 + (tan(c/2 + (d*x)/2)^5*(2*C*a^2 - B*b^2 + 2*C*b^2 - 2*B*a*b + C*a*b))/b^3 - (4*tan(c/2 + (d*x)/2)^3*(3*C*a^2 + C*b^2 - 3*B*a*b))/(3*b^3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1)) - (atan(((((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (4*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/b^10)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/(2*b^4))*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (4*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/b^10)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/(2*b^4))*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2)*1i)/(2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2))/b^9 - (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (4*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/b^10)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/(2*b^4))*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (4*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/b^10)*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/(2*b^4))*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2))/(2*b^4)))*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - C*a*b^2)*1i)/(b^4*d) - (a^3*atan(((a^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^3*((a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + (a^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^3*((a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2))/b^9 + (a^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^3*((a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) - (a^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^3*((a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*((a + b)*(a - b))^(1/2)*(B*b - C*a)*2i)/(d*(b^6 - a^2*b^4))","B"
794,1,4047,143,8.015034,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))),x)","\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,b\,\sin\left(c+d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{b^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2\,b\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{b^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,b\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2\,b^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{2\,b\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,a^2\,\mathrm{atan}\left(\frac{\left(8\,C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+C^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-C^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,C^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,B\,C\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,b-b^3\right)\,\left(-4\,B^2\,a^4\,b^3+4\,B^2\,a^2\,b^5+4\,B\,C\,a^5\,b^2-4\,B\,C\,a\,b^6-3\,C^2\,a^4\,b^3+2\,C^2\,a^2\,b^5+C^2\,b^7\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{b^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\left(8\,C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+C^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-C^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,C^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,B\,C\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,b-b^3\right)\,\left(-4\,B^2\,a^4\,b^3+4\,B^2\,a^2\,b^5+4\,B\,C\,a^5\,b^2-4\,B\,C\,a\,b^6-3\,C^2\,a^4\,b^3+2\,C^2\,a^2\,b^5+C^2\,b^7\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{b^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{b^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{2\,b\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{b^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,a^2\,\mathrm{atan}\left(\frac{\left(8\,C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+C^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-C^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,C^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,B\,C\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,b-b^3\right)\,\left(-4\,B^2\,a^4\,b^3+4\,B^2\,a^2\,b^5+4\,B\,C\,a^5\,b^2-4\,B\,C\,a\,b^6-3\,C^2\,a^4\,b^3+2\,C^2\,a^2\,b^5+C^2\,b^7\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{b^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\left(8\,C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+C^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-C^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,C^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,B\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,B\,C\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,b-b^3\right)\,\left(-4\,B^2\,a^4\,b^3+4\,B^2\,a^2\,b^5+4\,B\,C\,a^5\,b^2-4\,B\,C\,a\,b^6-3\,C^2\,a^4\,b^3+2\,C^2\,a^2\,b^5+C^2\,b^7\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{b^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(C*a*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*b*sin(c + d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(b^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(2*b*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(b^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*a^2*sin(2*c + 2*d*x))/(2*b*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a^3*sin(2*c + 2*d*x))/(2*b^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*a^2*sin(c + d*x))/(2*b*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*a^2*atan(((8*C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*C^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + C^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - C^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*C^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B*C*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*B*C*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*B*C*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a^2*b - b^3)*(C^2*b^7 + 4*B^2*a^2*b^5 - 4*B^2*a^4*b^3 + 2*C^2*a^2*b^5 - 3*C^2*a^4*b^3 - 4*B*C*a*b^6 + 4*B*C*a^5*b^2)))*((a + b)*(a - b))^(1/2)*1i)/(b^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a^3*atan(((8*C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*C^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + C^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - C^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*C^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B*C*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*B*C*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*B*C*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a^2*b - b^3)*(C^2*b^7 + 4*B^2*a^2*b^5 - 4*B^2*a^4*b^3 + 2*C^2*a^2*b^5 - 3*C^2*a^4*b^3 - 4*B*C*a*b^6 + 4*B*C*a^5*b^2)))*((a + b)*(a - b))^(1/2)*1i)/(b^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(b^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(2*b*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(b^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*a^2*atan(((8*C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*C^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + C^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - C^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*C^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B*C*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*B*C*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*B*C*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a^2*b - b^3)*(C^2*b^7 + 4*B^2*a^2*b^5 - 4*B^2*a^4*b^3 + 2*C^2*a^2*b^5 - 3*C^2*a^4*b^3 - 4*B*C*a*b^6 + 4*B*C*a^5*b^2)))*cos(2*c + 2*d*x)*((a + b)*(a - b))^(1/2)*1i)/(b^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a^3*atan(((8*C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*C^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + C^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - C^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*C^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*B*C*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*B*C*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*B*C*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*B*C*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a^2*b - b^3)*(C^2*b^7 + 4*B^2*a^2*b^5 - 4*B^2*a^4*b^3 + 2*C^2*a^2*b^5 - 3*C^2*a^4*b^3 - 4*B*C*a*b^6 + 4*B*C*a^5*b^2)))*cos(2*c + 2*d*x)*((a + b)*(a - b))^(1/2)*1i)/(b^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2))","B"
795,1,719,98,4.572851,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))),x)","\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{2\,B\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{C\,b\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}-\frac{C\,a^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{2\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,\left(a^2-b^2\right)}-\frac{2\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d\,\left(a^2-b^2\right)}-\frac{B\,a^3\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{C\,a^4\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{B\,a\,b\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{C\,a^2\,\mathrm{tan}\left(c+d\,x\right)}{b\,d\,\left(a^2-b^2\right)}-\frac{C\,a^2\,\ln\left(\frac{b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{b^2\,d\,\left(a^2-b^2\right)}+\frac{B\,a\,\ln\left(\frac{b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{b\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (2*B*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (C*b*tan(c + d*x))/(d*(a^2 - b^2)) - (C*a^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (2*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)) - (2*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d*(a^2 - b^2)) - (B*a^3*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)^(3/2)) + (C*a^4*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b^2*d*(a^2 - b^2)^(3/2)) + (B*a*b*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (C*a^2*tan(c + d*x))/(b*d*(a^2 - b^2)) - (C*a^2*log((b*sin(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(b^2*d*(a^2 - b^2)) + (B*a*log((b*sin(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(b*d*(a^2 - b^2))","B"
796,1,573,76,4.721786,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x)),x)","\frac{B\,a^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}-\frac{B\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{d\,\left(a^2-b^2\right)}-\frac{2\,C\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{B\,b^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,\left(a^2-b^2\right)}-\frac{C\,a^3\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{C\,a\,b\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{C\,a\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{b\,d\,\left(a^2-b^2\right)}","Not used",1,"(B*a^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) - (B*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(d*(a^2 - b^2)) - (2*C*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (B*b^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)) - (C*a^3*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)^(3/2)) + (C*a*b*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (C*a*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(b*d*(a^2 - b^2))","B"
797,1,573,67,4.773643,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{C\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{d\,\left(a^2-b^2\right)}+\frac{C\,a^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}-\frac{C\,b^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}-\frac{2\,B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d\,\left(a^2-b^2\right)}+\frac{B\,b^3\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d\,{\left(a^2-b^2\right)}^{3/2}}-\frac{B\,a\,b\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{B\,b\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{a\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (C*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(d*(a^2 - b^2)) + (C*a^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) - (C*b^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) - (2*B*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d*(a^2 - b^2)) + (B*b^3*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(a*d*(a^2 - b^2)^(3/2)) - (B*a*b*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (B*b*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(a*d*(a^2 - b^2))","B"
798,1,740,90,4.983479,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{2\,B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{B\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{B\,b^2\,\mathrm{atan}\left(\frac{-a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}-\frac{2\,B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{2\,C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{C\,a\,b\,\mathrm{atan}\left(\frac{-a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}","Not used",1,"(2*B*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) + (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) + (B*a^3*sin(c + d*x))/(d*(a^4 - a^2*b^2)) - (B*a*b^2*sin(c + d*x))/(d*(a^4 - a^2*b^2)) + (B*b^2*atan((b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - a^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i)/(a^6*cos(c/2 + (d*x)/2) + a^2*b^4*cos(c/2 + (d*x)/2) - 2*a^4*b^2*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2)) - (2*B*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) - (2*C*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) - (C*a*b*atan((b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - a^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i)/(a^6*cos(c/2 + (d*x)/2) + a^2*b^4*cos(c/2 + (d*x)/2) - 2*a^4*b^2*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2))","B"
799,1,3740,134,8.023736,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a-2\,B\,b+2\,C\,a\right)}{a^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a+2\,B\,b-2\,C\,a\right)}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)}{2\,a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,a^3}-\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)}{2\,a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,a^3}}{\frac{16\,\left(-B^3\,a^5\,b^3+2\,B^3\,a^4\,b^4-5\,B^3\,a^3\,b^5+6\,B^3\,a^2\,b^6-6\,B^3\,a\,b^7+4\,B^3\,b^8+B^2\,C\,a^6\,b^2-2\,B^2\,C\,a^5\,b^3+9\,B^2\,C\,a^4\,b^4-12\,B^2\,C\,a^3\,b^5+16\,B^2\,C\,a^2\,b^6-12\,B^2\,C\,a\,b^7-4\,B\,C^2\,a^5\,b^3+6\,B\,C^2\,a^4\,b^4-14\,B\,C^2\,a^3\,b^5+12\,B\,C^2\,a^2\,b^6+4\,C^3\,a^4\,b^4-4\,C^3\,a^3\,b^5\right)}{a^6}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)}{2\,a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)}{2\,a^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)}{2\,a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)}{2\,a^3}}\right)\,\left(1{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,C\,a\,b+2{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{a^3\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}}{\frac{16\,\left(-B^3\,a^5\,b^3+2\,B^3\,a^4\,b^4-5\,B^3\,a^3\,b^5+6\,B^3\,a^2\,b^6-6\,B^3\,a\,b^7+4\,B^3\,b^8+B^2\,C\,a^6\,b^2-2\,B^2\,C\,a^5\,b^3+9\,B^2\,C\,a^4\,b^4-12\,B^2\,C\,a^3\,b^5+16\,B^2\,C\,a^2\,b^6-12\,B^2\,C\,a\,b^7-4\,B\,C^2\,a^5\,b^3+6\,B\,C^2\,a^4\,b^4-14\,B\,C^2\,a^3\,b^5+12\,B\,C^2\,a^2\,b^6+4\,C^3\,a^4\,b^4-4\,C^3\,a^3\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^7-3\,B^2\,a^6\,b+7\,B^2\,a^5\,b^2-13\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-16\,B^2\,a^2\,b^5+16\,B^2\,a\,b^6-8\,B^2\,b^7-4\,B\,C\,a^6\,b+12\,B\,C\,a^5\,b^2-20\,B\,C\,a^4\,b^3+28\,B\,C\,a^3\,b^4-32\,B\,C\,a^2\,b^5+16\,B\,C\,a\,b^6+4\,C^2\,a^5\,b^2-12\,C^2\,a^4\,b^3+16\,C^2\,a^3\,b^4-8\,C^2\,a^2\,b^5\right)}{a^4}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{10}+4\,B\,a^6\,b^4-6\,B\,a^7\,b^3+2\,B\,a^8\,b^2-4\,C\,a^7\,b^3+8\,C\,a^8\,b^2-2\,B\,a^9\,b-4\,C\,a^9\,b\right)}{a^6}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,2{}\mathrm{i}}{d\,\left(a^5-a^3\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(B*a - 2*B*b + 2*C*a))/a^2 - (tan(c/2 + (d*x)/2)^3*(B*a + 2*B*b - 2*C*a))/a^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 - (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(B*a^2*1i + B*b^2*2i - C*a*b*2i))/(2*a^3) + (8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4)*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*1i)/(2*a^3) - (((((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 + (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(B*a^2*1i + B*b^2*2i - C*a*b*2i))/(2*a^3) - (8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4)*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*1i)/(2*a^3))/((16*(4*B^3*b^8 - 6*B^3*a*b^7 + 6*B^3*a^2*b^6 - 5*B^3*a^3*b^5 + 2*B^3*a^4*b^4 - B^3*a^5*b^3 - 4*C^3*a^3*b^5 + 4*C^3*a^4*b^4 - 12*B^2*C*a*b^7 + 12*B*C^2*a^2*b^6 - 14*B*C^2*a^3*b^5 + 6*B*C^2*a^4*b^4 - 4*B*C^2*a^5*b^3 + 16*B^2*C*a^2*b^6 - 12*B^2*C*a^3*b^5 + 9*B^2*C*a^4*b^4 - 2*B^2*C*a^5*b^3 + B^2*C*a^6*b^2))/a^6 + (((((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 - (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(B*a^2*1i + B*b^2*2i - C*a*b*2i))/(2*a^3) + (8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4)*(B*a^2*1i + B*b^2*2i - C*a*b*2i))/(2*a^3) + (((((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 + (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(B*a^2*1i + B*b^2*2i - C*a*b*2i))/(2*a^3) - (8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4)*(B*a^2*1i + B*b^2*2i - C*a*b*2i))/(2*a^3)))*(B*a^2*1i + B*b^2*2i - C*a*b*2i)*1i)/(a^3*d) - (b^2*atan(((b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4 + (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*1i)/(a^5 - a^3*b^2) + (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4 - (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*1i)/(a^5 - a^3*b^2))/((16*(4*B^3*b^8 - 6*B^3*a*b^7 + 6*B^3*a^2*b^6 - 5*B^3*a^3*b^5 + 2*B^3*a^4*b^4 - B^3*a^5*b^3 - 4*C^3*a^3*b^5 + 4*C^3*a^4*b^4 - 12*B^2*C*a*b^7 + 12*B*C^2*a^2*b^6 - 14*B*C^2*a^3*b^5 + 6*B*C^2*a^4*b^4 - 4*B*C^2*a^5*b^3 + 16*B^2*C*a^2*b^6 - 12*B^2*C*a^3*b^5 + 9*B^2*C*a^4*b^4 - 2*B^2*C*a^5*b^3 + B^2*C*a^6*b^2))/a^6 + (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4 + (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2) - (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*a^7 - 8*B^2*b^7 + 16*B^2*a*b^6 - 3*B^2*a^6*b - 16*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 13*B^2*a^4*b^3 + 7*B^2*a^5*b^2 - 8*C^2*a^2*b^5 + 16*C^2*a^3*b^4 - 12*C^2*a^4*b^3 + 4*C^2*a^5*b^2 + 16*B*C*a*b^6 - 4*B*C*a^6*b - 32*B*C*a^2*b^5 + 28*B*C*a^3*b^4 - 20*B*C*a^4*b^3 + 12*B*C*a^5*b^2))/a^4 - (b^2*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*(2*B*a^10 + 4*B*a^6*b^4 - 6*B*a^7*b^3 + 2*B*a^8*b^2 - 4*C*a^7*b^3 + 8*C*a^8*b^2 - 2*B*a^9*b - 4*C*a^9*b))/a^6 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2)))*((a + b)*(a - b))^(1/2)*(B*b - C*a)*2i)/(d*(a^5 - a^3*b^2))","B"
800,1,4572,178,8.921360,"\text{Not used}","int((cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a^2+2\,B\,b^2+C\,a^2-B\,a\,b-2\,C\,a\,b\right)}{a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,B\,a^2+2\,B\,b^2-C\,a^2+B\,a\,b-2\,C\,a\,b\right)}{a^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a^2-3\,C\,a\,b+3\,B\,b^2\right)}{3\,a^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}-\frac{\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,a^4}\right)}{2\,a^4}+\frac{\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}+\frac{\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,a^4}\right)}{2\,a^4}}{\frac{16\,\left(-B^3\,a^5\,b^6+2\,B^3\,a^4\,b^7-5\,B^3\,a^3\,b^8+6\,B^3\,a^2\,b^9-6\,B^3\,a\,b^{10}+4\,B^3\,b^{11}+3\,B^2\,C\,a^6\,b^5-6\,B^2\,C\,a^5\,b^6+15\,B^2\,C\,a^4\,b^7-18\,B^2\,C\,a^3\,b^8+18\,B^2\,C\,a^2\,b^9-12\,B^2\,C\,a\,b^{10}-3\,B\,C^2\,a^7\,b^4+6\,B\,C^2\,a^6\,b^5-15\,B\,C^2\,a^5\,b^6+18\,B\,C^2\,a^4\,b^7-18\,B\,C^2\,a^3\,b^8+12\,B\,C^2\,a^2\,b^9+C^3\,a^8\,b^3-2\,C^3\,a^7\,b^4+5\,C^3\,a^6\,b^5-6\,C^3\,a^5\,b^6+6\,C^3\,a^4\,b^7-4\,C^3\,a^3\,b^8\right)}{a^9}+\frac{\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}-\frac{\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,a^4}\right)\,1{}\mathrm{i}}{2\,a^4}-\frac{\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}+\frac{\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,a^4}\right)\,1{}\mathrm{i}}{2\,a^4}}\right)\,\left(a^2+2\,b^2\right)\,\left(B\,b-C\,a\right)}{a^4\,d}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(B\,b-C\,a\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(B\,b-C\,a\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-B^3\,a^5\,b^6+2\,B^3\,a^4\,b^7-5\,B^3\,a^3\,b^8+6\,B^3\,a^2\,b^9-6\,B^3\,a\,b^{10}+4\,B^3\,b^{11}+3\,B^2\,C\,a^6\,b^5-6\,B^2\,C\,a^5\,b^6+15\,B^2\,C\,a^4\,b^7-18\,B^2\,C\,a^3\,b^8+18\,B^2\,C\,a^2\,b^9-12\,B^2\,C\,a\,b^{10}-3\,B\,C^2\,a^7\,b^4+6\,B\,C^2\,a^6\,b^5-15\,B\,C^2\,a^5\,b^6+18\,B\,C^2\,a^4\,b^7-18\,B\,C^2\,a^3\,b^8+12\,B\,C^2\,a^2\,b^9+C^3\,a^8\,b^3-2\,C^3\,a^7\,b^4+5\,C^3\,a^6\,b^5-6\,C^3\,a^5\,b^6+6\,C^3\,a^4\,b^7-4\,C^3\,a^3\,b^8\right)}{a^9}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(B\,b-C\,a\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-B^2\,a^7\,b^2+3\,B^2\,a^6\,b^3-7\,B^2\,a^5\,b^4+13\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+16\,B^2\,a^2\,b^7-16\,B^2\,a\,b^8+8\,B^2\,b^9+2\,B\,C\,a^8\,b-6\,B\,C\,a^7\,b^2+14\,B\,C\,a^6\,b^3-26\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-32\,B\,C\,a^3\,b^6+32\,B\,C\,a^2\,b^7-16\,B\,C\,a\,b^8-C^2\,a^9+3\,C^2\,a^8\,b-7\,C^2\,a^7\,b^2+13\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+16\,C^2\,a^4\,b^5-16\,C^2\,a^3\,b^6+8\,C^2\,a^2\,b^7\right)}{a^6}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,C\,a^{13}-4\,B\,a^8\,b^5+6\,B\,a^9\,b^4-2\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2+4\,C\,a^9\,b^4-6\,C\,a^{10}\,b^3+2\,C\,a^{11}\,b^2-2\,B\,a^{12}\,b-2\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(B\,b-C\,a\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*B*a^2 + 2*B*b^2 + C*a^2 - B*a*b - 2*C*a*b))/a^3 + (tan(c/2 + (d*x)/2)^5*(2*B*a^2 + 2*B*b^2 - C*a^2 + B*a*b - 2*C*a*b))/a^3 + (4*tan(c/2 + (d*x)/2)^3*(B*a^2 + 3*B*b^2 - 3*C*a*b))/(3*a^3))/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) - (atan((((a^2 + 2*b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 - (((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 - (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*(a^2 + 2*b^2)*(B*b - C*a)*1i)/(2*a^4)))/(2*a^4) + ((a^2 + 2*b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 + (((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 + (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*(a^2 + 2*b^2)*(B*b - C*a)*1i)/(2*a^4)))/(2*a^4))/((16*(4*B^3*b^11 - 6*B^3*a*b^10 + 6*B^3*a^2*b^9 - 5*B^3*a^3*b^8 + 2*B^3*a^4*b^7 - B^3*a^5*b^6 - 4*C^3*a^3*b^8 + 6*C^3*a^4*b^7 - 6*C^3*a^5*b^6 + 5*C^3*a^6*b^5 - 2*C^3*a^7*b^4 + C^3*a^8*b^3 - 12*B^2*C*a*b^10 + 12*B*C^2*a^2*b^9 - 18*B*C^2*a^3*b^8 + 18*B*C^2*a^4*b^7 - 15*B*C^2*a^5*b^6 + 6*B*C^2*a^6*b^5 - 3*B*C^2*a^7*b^4 + 18*B^2*C*a^2*b^9 - 18*B^2*C*a^3*b^8 + 15*B^2*C*a^4*b^7 - 6*B^2*C*a^5*b^6 + 3*B^2*C*a^6*b^5))/a^9 + ((a^2 + 2*b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 - (((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 - (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*(a^2 + 2*b^2)*(B*b - C*a)*1i)/(2*a^4))*1i)/(2*a^4) - ((a^2 + 2*b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 + (((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 + (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*(a^2 + 2*b^2)*(B*b - C*a)*1i)/(2*a^4))*1i)/(2*a^4)))*(a^2 + 2*b^2)*(B*b - C*a))/(a^4*d) - (b^3*atan(((b^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 + (b^3*((a + b)*(a - b))^(1/2)*((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 + (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(B*b - C*a))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 - (b^3*((a + b)*(a - b))^(1/2)*((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 - (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(B*b - C*a))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((16*(4*B^3*b^11 - 6*B^3*a*b^10 + 6*B^3*a^2*b^9 - 5*B^3*a^3*b^8 + 2*B^3*a^4*b^7 - B^3*a^5*b^6 - 4*C^3*a^3*b^8 + 6*C^3*a^4*b^7 - 6*C^3*a^5*b^6 + 5*C^3*a^6*b^5 - 2*C^3*a^7*b^4 + C^3*a^8*b^3 - 12*B^2*C*a*b^10 + 12*B*C^2*a^2*b^9 - 18*B*C^2*a^3*b^8 + 18*B*C^2*a^4*b^7 - 15*B*C^2*a^5*b^6 + 6*B*C^2*a^6*b^5 - 3*B*C^2*a^7*b^4 + 18*B^2*C*a^2*b^9 - 18*B^2*C*a^3*b^8 + 15*B^2*C*a^4*b^7 - 6*B^2*C*a^5*b^6 + 3*B^2*C*a^6*b^5))/a^9 - (b^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 + (b^3*((a + b)*(a - b))^(1/2)*((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 + (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(B*b - C*a))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) + (b^3*((a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^9 - C^2*a^9 - 16*B^2*a*b^8 + 3*C^2*a^8*b + 16*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 13*B^2*a^4*b^5 - 7*B^2*a^5*b^4 + 3*B^2*a^6*b^3 - B^2*a^7*b^2 + 8*C^2*a^2*b^7 - 16*C^2*a^3*b^6 + 16*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 13*C^2*a^6*b^3 - 7*C^2*a^7*b^2 - 16*B*C*a*b^8 + 2*B*C*a^8*b + 32*B*C*a^2*b^7 - 32*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 26*B*C*a^5*b^4 + 14*B*C*a^6*b^3 - 6*B*C*a^7*b^2))/a^6 - (b^3*((a + b)*(a - b))^(1/2)*((8*(2*C*a^13 - 4*B*a^8*b^5 + 6*B*a^9*b^4 - 2*B*a^10*b^3 + 2*B*a^11*b^2 + 4*C*a^9*b^4 - 6*C*a^10*b^3 + 2*C*a^11*b^2 - 2*B*a^12*b - 2*C*a^12*b))/a^9 - (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(B*b - C*a))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*((a + b)*(a - b))^(1/2)*(B*b - C*a)*2i)/(d*(a^6 - a^4*b^2))","B"
801,1,6677,272,13.700618,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^2),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^4-2\,B\,b^4+C\,b^4+2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b+3\,C\,a\,b^3-3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-6\,C\,a^4+4\,B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+C\,b^4\right)}{b\,\left(a\,b^2-b^3\right)\,\left(a+b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4+6\,C\,a^4+C\,b^4-2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b-3\,C\,a\,b^3+3\,C\,a^3\,b\right)}{b^3\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)}{2\,b^4}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)}{2\,b^4}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)}{2\,b^4}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)}{2\,b^4}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)}{2\,b^4}}\right)\,\left(6\,C\,a^2-4\,B\,a\,b+C\,b^2\right)\,1{}\mathrm{i}}{b^4\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}-\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^5*(6*C*a^4 - 2*B*b^4 + C*b^4 + 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b + 3*C*a*b^3 - 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(C*b^4 - 6*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + 4*B*a^3*b))/(b*(a*b^2 - b^3)*(a + b)) + (tan(c/2 + (d*x)/2)*(2*B*b^4 + 6*C*a^4 + C*b^4 - 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b - 3*C*a*b^3 + 3*C*a^3*b))/(b^3*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(3*a + b) - tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) - (atan(((((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(6*C*a^2 + C*b^2 - 4*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(6*C*a^2 + C*b^2 - 4*B*a*b))/(2*b^4))*(6*C*a^2 + C*b^2 - 4*B*a*b)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(6*C*a^2 + C*b^2 - 4*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(6*C*a^2 + C*b^2 - 4*B*a*b))/(2*b^4))*(6*C*a^2 + C*b^2 - 4*B*a*b)*1i)/(2*b^4))/((16*(108*C^3*a^11 - 54*C^3*a^10*b - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 - 216*B*C^2*a^10*b - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(6*C*a^2 + C*b^2 - 4*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(6*C*a^2 + C*b^2 - 4*B*a*b))/(2*b^4))*(6*C*a^2 + C*b^2 - 4*B*a*b))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(6*C*a^2 + C*b^2 - 4*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(6*C*a^2 + C*b^2 - 4*B*a*b))/(2*b^4))*(6*C*a^2 + C*b^2 - 4*B*a*b))/(2*b^4)))*(6*C*a^2 + C*b^2 - 4*B*a*b)*1i)/(b^4*d) - (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*C^3*a^11 - 54*C^3*a^10*b - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 - 216*B*C^2*a^10*b - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) - (a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
802,1,5436,164,12.680631,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a^2\,b-C\,b^3-2\,C\,a^3+C\,a\,b^2+C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,b^3-2\,C\,a^3+B\,a^2\,b+C\,a\,b^2-C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,\left(B\,b-2\,C\,a\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,\left(B\,b-2\,C\,a\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}}{\frac{64\,\left(-B^3\,a^5\,b^3+B^3\,a^4\,b^4+3\,B^3\,a^3\,b^5-2\,B^3\,a^2\,b^6-2\,B^3\,a\,b^7+6\,B^2\,C\,a^6\,b^2-5\,B^2\,C\,a^5\,b^3-17\,B^2\,C\,a^4\,b^4+9\,B^2\,C\,a^3\,b^5+11\,B^2\,C\,a^2\,b^6-12\,B\,C^2\,a^7\,b+8\,B\,C^2\,a^6\,b^2+32\,B\,C^2\,a^5\,b^3-13\,B\,C^2\,a^4\,b^4-20\,B\,C^2\,a^3\,b^5+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,\left(B\,b-2\,C\,a\right)}{b^3}\right)}{b^3}-\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,\left(B\,b-2\,C\,a\right)}{b^3}\right)}{b^3}}\right)\,\left(B\,b-2\,C\,a\right)\,2{}\mathrm{i}}{b^3\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(-B^3\,a^5\,b^3+B^3\,a^4\,b^4+3\,B^3\,a^3\,b^5-2\,B^3\,a^2\,b^6-2\,B^3\,a\,b^7+6\,B^2\,C\,a^6\,b^2-5\,B^2\,C\,a^5\,b^3-17\,B^2\,C\,a^4\,b^4+9\,B^2\,C\,a^3\,b^5+11\,B^2\,C\,a^2\,b^6-12\,B\,C^2\,a^7\,b+8\,B\,C^2\,a^6\,b^2+32\,B\,C^2\,a^5\,b^3-13\,B\,C^2\,a^4\,b^4-20\,B\,C^2\,a^3\,b^5+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}-\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(B*a^2*b - C*b^3 - 2*C*a^3 + C*a*b^2 + C*a^2*b))/(b^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)*(C*b^3 - 2*C*a^3 + B*a^2*b + C*a*b^2 - C*a^2*b))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) - 2*a*tan(c/2 + (d*x)/2)^2)) + (atan((((B*b - 2*C*a)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*(B*b - 2*C*a))/b^3)*1i)/b^3 + ((B*b - 2*C*a)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*(B*b - 2*C*a))/b^3)*1i)/b^3)/((64*(8*C^3*a^8 - 2*B^3*a*b^7 - 4*C^3*a^7*b - 2*B^3*a^2*b^6 + 3*B^3*a^3*b^5 + B^3*a^4*b^4 - B^3*a^5*b^3 + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 - 12*B*C^2*a^7*b - 20*B*C^2*a^3*b^5 - 13*B*C^2*a^4*b^4 + 32*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 11*B^2*C*a^2*b^6 + 9*B^2*C*a^3*b^5 - 17*B^2*C*a^4*b^4 - 5*B^2*C*a^5*b^3 + 6*B^2*C*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + ((B*b - 2*C*a)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*(B*b - 2*C*a))/b^3))/b^3 - ((B*b - 2*C*a)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*(B*b - 2*C*a))/b^3))/b^3))*(B*b - 2*C*a)*2i)/(b^3*d) + (a*atan(((a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*C^3*a^8 - 2*B^3*a*b^7 - 4*C^3*a^7*b - 2*B^3*a^2*b^6 + 3*B^3*a^3*b^5 + B^3*a^4*b^4 - B^3*a^5*b^3 + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 - 12*B*C^2*a^7*b - 20*B*C^2*a^3*b^5 - 13*B*C^2*a^4*b^4 + 32*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 11*B^2*C*a^2*b^6 + 9*B^2*C*a^3*b^5 - 17*B^2*C*a^4*b^4 - 5*B^2*C*a^5*b^3 + 6*B^2*C*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) - (a*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
803,1,3751,131,11.898107,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^2),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)\,1{}\mathrm{i}}{b^2}-\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)\,1{}\mathrm{i}}{b^2}}{\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)}{b^2}-\frac{64\,\left(B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\left(\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)}{b^2}}\right)\,2{}\mathrm{i}}{b^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"- (C*atan(((C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 - (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 - (C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 + (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2)/((C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 - (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2 - (64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 - 3*B*C^2*a*b^4 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2 + (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2))*2i)/(b^2*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 - 3*B*C^2*a*b^4 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(C*a^2 - B*a*b))/(d*(a + b)*(a*b - b^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
804,1,106,100,4.058800,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^2,x)","\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a-b}}{\sqrt{a+b}}\right)\,\left(B\,a-C\,b\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*atanh((tan(c/2 + (d*x)/2)*(a - b)^(1/2))/(a + b)^(1/2))*(B*a - C*b))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (2*tan(c/2 + (d*x)/2)*(B*b - C*a))/(d*(a + b)*(a - b)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
805,1,3763,124,12.091351,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\frac{2\,B\,\mathrm{atan}\left(\frac{\frac{B\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)}{a^2}-\frac{B\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)}{a^2}}{\frac{64\,\left(2\,B^3\,a^4\,b+2\,B^3\,a^3\,b^2-3\,B^3\,a^2\,b^3-B^3\,a\,b^4+B^3\,b^5-B^2\,C\,a^5-3\,B^2\,C\,a^4\,b+B^2\,C\,a^3\,b^2+B^2\,C\,a^2\,b^3+B\,C^2\,a^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{B\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{B\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2-C\,a\,b\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,B^3\,a^4\,b+2\,B^3\,a^3\,b^2-3\,B^3\,a^2\,b^3-B^3\,a\,b^4+B^3\,b^5-B^2\,C\,a^5-3\,B^2\,C\,a^4\,b+B^2\,C\,a^3\,b^2+B^2\,C\,a^2\,b^3+B\,C^2\,a^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"(2*B*atan(((B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 + (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2 - (B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 - (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2)/((64*(B^3*b^5 + B*C^2*a^5 - B^2*C*a^5 - B^3*a*b^4 + 2*B^3*a^4*b - 3*B^3*a^2*b^3 + 2*B^3*a^3*b^2 - 3*B^2*C*a^4*b + B^2*C*a^2*b^3 + B^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 + (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 + (B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2 - (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)))/(a^2*d) + (atan(((((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(B^3*b^5 + B*C^2*a^5 - B^2*C*a^5 - B^3*a*b^4 + 2*B^3*a^4*b - 3*B^3*a^2*b^3 + 2*B^3*a^3*b^2 - 3*B^2*C*a^4*b + B^2*C*a^2*b^3 + B^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) - (((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(B*b^2 - C*a*b))/(d*(a + b)*(a*b - a^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
806,1,3264,180,9.045109,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a\,b^2-2\,B\,b^3-B\,a^3+B\,a^2\,b+C\,a\,b^2\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a^3-2\,B\,b^3-B\,a\,b^2+B\,a^2\,b+C\,a\,b^2\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(2\,B\,b-C\,a\right)\,1{}\mathrm{i}}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b\,2{}\mathrm{i}-C\,a\,1{}\mathrm{i}\right)}{a^3\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,B^3\,a^4\,b^4+6\,B^3\,a^3\,b^5-20\,B^3\,a^2\,b^6-4\,B^3\,a\,b^7+8\,B^3\,b^8-20\,B^2\,C\,a^5\,b^3-13\,B^2\,C\,a^4\,b^4+32\,B^2\,C\,a^3\,b^5+8\,B^2\,C\,a^2\,b^6-12\,B^2\,C\,a\,b^7+11\,B\,C^2\,a^6\,b^2+9\,B\,C^2\,a^5\,b^3-17\,B\,C^2\,a^4\,b^4-5\,B\,C^2\,a^3\,b^5+6\,B\,C^2\,a^2\,b^6-2\,C^3\,a^7\,b-2\,C^3\,a^6\,b^2+3\,C^3\,a^5\,b^3+C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(B*a*b^2 - 2*B*b^3 - B*a^3 + B*a^2*b + C*a*b^2))/(a^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(B*a^3 - 2*B*b^3 - B*a*b^2 + B*a^2*b + C*a*b^2))/(a^2*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) + 2*b*tan(c/2 + (d*x)/2)^2)) + (log(tan(c/2 + (d*x)/2) - 1i)*(2*B*b - C*a)*1i)/(a^3*d) - (log(tan(c/2 + (d*x)/2) + 1i)*(B*b*2i - C*a*1i))/(a^3*d) - (b*atan(((b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*B^3*b^8 - 4*B^3*a*b^7 - 2*C^3*a^7*b - 20*B^3*a^2*b^6 + 6*B^3*a^3*b^5 + 12*B^3*a^4*b^4 - C^3*a^3*b^5 + C^3*a^4*b^4 + 3*C^3*a^5*b^3 - 2*C^3*a^6*b^2 - 12*B^2*C*a*b^7 + 6*B*C^2*a^2*b^6 - 5*B*C^2*a^3*b^5 - 17*B*C^2*a^4*b^4 + 9*B*C^2*a^5*b^3 + 11*B*C^2*a^6*b^2 + 8*B^2*C*a^2*b^6 + 32*B^2*C*a^3*b^5 - 13*B^2*C*a^4*b^4 - 20*B^2*C*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
807,1,6730,261,13.927809,"\text{Not used}","int((cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B\,a^4+6\,B\,b^4-2\,C\,a^4-5\,B\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+3\,B\,a^3\,b-4\,C\,a\,b^3+2\,C\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a^4+6\,B\,b^4+2\,C\,a^4-5\,B\,a^2\,b^2-2\,C\,a^2\,b^2+3\,B\,a\,b^3-3\,B\,a^3\,b-4\,C\,a\,b^3+2\,C\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a^4-2\,C\,a^3\,b+3\,B\,a^2\,b^2+4\,C\,a\,b^3-6\,B\,b^4\right)}{a\,\left(a^2\,b-a^3\right)\,\left(a+b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(a+3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,a^4}}{\frac{16\,\left(4\,B^3\,a^8\,b^3-4\,B^3\,a^7\,b^4+41\,B^3\,a^6\,b^5-9\,B^3\,a^5\,b^6+63\,B^3\,a^4\,b^7+81\,B^3\,a^3\,b^8-216\,B^3\,a^2\,b^9-54\,B^3\,a\,b^{10}+108\,B^3\,b^{11}-3\,B^2\,C\,a^9\,b^2+3\,B^2\,C\,a^8\,b^3-63\,B^2\,C\,a^7\,b^4+15\,B^2\,C\,a^6\,b^5-186\,B^2\,C\,a^5\,b^6-162\,B^2\,C\,a^4\,b^7+468\,B^2\,C\,a^3\,b^8+108\,B^2\,C\,a^2\,b^9-216\,B^2\,C\,a\,b^{10}+24\,B\,C^2\,a^8\,b^3-6\,B\,C^2\,a^7\,b^4+168\,B\,C^2\,a^6\,b^5+108\,B\,C^2\,a^5\,b^6-336\,B\,C^2\,a^4\,b^7-72\,B\,C^2\,a^3\,b^8+144\,B\,C^2\,a^2\,b^9-48\,C^3\,a^7\,b^4-24\,C^3\,a^6\,b^5+80\,C^3\,a^5\,b^6+16\,C^3\,a^4\,b^7-32\,C^3\,a^3\,b^8\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)}{2\,a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)}{2\,a^4}}\right)\,\left(1{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,C\,a\,b+6{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{a^4\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(4\,B^3\,a^8\,b^3-4\,B^3\,a^7\,b^4+41\,B^3\,a^6\,b^5-9\,B^3\,a^5\,b^6+63\,B^3\,a^4\,b^7+81\,B^3\,a^3\,b^8-216\,B^3\,a^2\,b^9-54\,B^3\,a\,b^{10}+108\,B^3\,b^{11}-3\,B^2\,C\,a^9\,b^2+3\,B^2\,C\,a^8\,b^3-63\,B^2\,C\,a^7\,b^4+15\,B^2\,C\,a^6\,b^5-186\,B^2\,C\,a^5\,b^6-162\,B^2\,C\,a^4\,b^7+468\,B^2\,C\,a^3\,b^8+108\,B^2\,C\,a^2\,b^9-216\,B^2\,C\,a\,b^{10}+24\,B\,C^2\,a^8\,b^3-6\,B\,C^2\,a^7\,b^4+168\,B\,C^2\,a^6\,b^5+108\,B\,C^2\,a^5\,b^6-336\,B\,C^2\,a^4\,b^7-72\,B\,C^2\,a^3\,b^8+144\,B\,C^2\,a^2\,b^9-48\,C^3\,a^7\,b^4-24\,C^3\,a^6\,b^5+80\,C^3\,a^5\,b^6+16\,C^3\,a^4\,b^7-32\,C^3\,a^3\,b^8\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^{10}-2\,B^2\,a^9\,b+11\,B^2\,a^8\,b^2-20\,B^2\,a^7\,b^3+23\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+17\,B^2\,a^4\,b^6+120\,B^2\,a^3\,b^7-120\,B^2\,a^2\,b^8-72\,B^2\,a\,b^9+72\,B^2\,b^{10}-8\,B\,C\,a^9\,b+16\,B\,C\,a^8\,b^2-40\,B\,C\,a^7\,b^3+64\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5-176\,B\,C\,a^4\,b^6+176\,B\,C\,a^3\,b^7+96\,B\,C\,a^2\,b^8-96\,B\,C\,a\,b^9+16\,C^2\,a^8\,b^2-32\,C^2\,a^7\,b^3+20\,C^2\,a^6\,b^4+64\,C^2\,a^5\,b^5-64\,C^2\,a^4\,b^6-32\,C^2\,a^3\,b^7+32\,C^2\,a^2\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{15}-12\,B\,a^8\,b^7+6\,B\,a^9\,b^6+28\,B\,a^{10}\,b^5-14\,B\,a^{11}\,b^4-16\,B\,a^{12}\,b^3+6\,B\,a^{13}\,b^2+8\,C\,a^9\,b^6-4\,C\,a^{10}\,b^5-20\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+12\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-4\,B\,a^2\,b-2\,C\,a\,b^2+3\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"(atan(((((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(B*a^2*1i + B*b^2*6i - C*a*b*4i))/(2*a^4))*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*1i)/(2*a^4) + (((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(B*a^2*1i + B*b^2*6i - C*a*b*4i))/(2*a^4))*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*1i)/(2*a^4))/((16*(108*B^3*b^11 - 54*B^3*a*b^10 - 216*B^3*a^2*b^9 + 81*B^3*a^3*b^8 + 63*B^3*a^4*b^7 - 9*B^3*a^5*b^6 + 41*B^3*a^6*b^5 - 4*B^3*a^7*b^4 + 4*B^3*a^8*b^3 - 32*C^3*a^3*b^8 + 16*C^3*a^4*b^7 + 80*C^3*a^5*b^6 - 24*C^3*a^6*b^5 - 48*C^3*a^7*b^4 - 216*B^2*C*a*b^10 + 144*B*C^2*a^2*b^9 - 72*B*C^2*a^3*b^8 - 336*B*C^2*a^4*b^7 + 108*B*C^2*a^5*b^6 + 168*B*C^2*a^6*b^5 - 6*B*C^2*a^7*b^4 + 24*B*C^2*a^8*b^3 + 108*B^2*C*a^2*b^9 + 468*B^2*C*a^3*b^8 - 162*B^2*C*a^4*b^7 - 186*B^2*C*a^5*b^6 + 15*B^2*C*a^6*b^5 - 63*B^2*C*a^7*b^4 + 3*B^2*C*a^8*b^3 - 3*B^2*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(B*a^2*1i + B*b^2*6i - C*a*b*4i))/(2*a^4))*(B*a^2*1i + B*b^2*6i - C*a*b*4i))/(2*a^4) + (((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(B*a^2*1i + B*b^2*6i - C*a*b*4i))/(2*a^4))*(B*a^2*1i + B*b^2*6i - C*a*b*4i))/(2*a^4)))*(B*a^2*1i + B*b^2*6i - C*a*b*4i)*1i)/(a^4*d) - ((tan(c/2 + (d*x)/2)^5*(B*a^4 + 6*B*b^4 - 2*C*a^4 - 5*B*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 3*B*a^3*b - 4*C*a*b^3 + 2*C*a^3*b))/((a^3*b - a^4)*(a + b)) + (tan(c/2 + (d*x)/2)*(B*a^4 + 6*B*b^4 + 2*C*a^4 - 5*B*a^2*b^2 - 2*C*a^2*b^2 + 3*B*a*b^3 - 3*B*a^3*b - 4*C*a*b^3 + 2*C*a^3*b))/((a^3*b - a^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(B*a^4 - 6*B*b^4 + 3*B*a^2*b^2 + 4*C*a*b^3 - 2*C*a^3*b))/(a*(a^2*b - a^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) - tan(c/2 + (d*x)/2)^6*(a - b))) + (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^2*((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^2*((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(108*B^3*b^11 - 54*B^3*a*b^10 - 216*B^3*a^2*b^9 + 81*B^3*a^3*b^8 + 63*B^3*a^4*b^7 - 9*B^3*a^5*b^6 + 41*B^3*a^6*b^5 - 4*B^3*a^7*b^4 + 4*B^3*a^8*b^3 - 32*C^3*a^3*b^8 + 16*C^3*a^4*b^7 + 80*C^3*a^5*b^6 - 24*C^3*a^6*b^5 - 48*C^3*a^7*b^4 - 216*B^2*C*a*b^10 + 144*B*C^2*a^2*b^9 - 72*B*C^2*a^3*b^8 - 336*B*C^2*a^4*b^7 + 108*B*C^2*a^5*b^6 + 168*B*C^2*a^6*b^5 - 6*B*C^2*a^7*b^4 + 24*B*C^2*a^8*b^3 + 108*B^2*C*a^2*b^9 + 468*B^2*C*a^3*b^8 - 162*B^2*C*a^4*b^7 - 186*B^2*C*a^5*b^6 + 15*B^2*C*a^6*b^5 - 63*B^2*C*a^7*b^4 + 3*B^2*C*a^8*b^3 - 3*B^2*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (b^2*((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^2*((8*tan(c/2 + (d*x)/2)*(B^2*a^10 + 72*B^2*b^10 - 72*B^2*a*b^9 - 2*B^2*a^9*b - 120*B^2*a^2*b^8 + 120*B^2*a^3*b^7 + 17*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 23*B^2*a^6*b^4 - 20*B^2*a^7*b^3 + 11*B^2*a^8*b^2 + 32*C^2*a^2*b^8 - 32*C^2*a^3*b^7 - 64*C^2*a^4*b^6 + 64*C^2*a^5*b^5 + 20*C^2*a^6*b^4 - 32*C^2*a^7*b^3 + 16*C^2*a^8*b^2 - 96*B*C*a*b^9 - 8*B*C*a^9*b + 96*B*C*a^2*b^8 + 176*B*C*a^3*b^7 - 176*B*C*a^4*b^6 - 40*B*C*a^5*b^5 + 64*B*C*a^6*b^4 - 40*B*C*a^7*b^3 + 16*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^2*((8*(2*B*a^15 - 12*B*a^8*b^7 + 6*B*a^9*b^6 + 28*B*a^10*b^5 - 14*B*a^11*b^4 - 16*B*a^12*b^3 + 6*B*a^13*b^2 + 8*C*a^9*b^6 - 4*C*a^10*b^5 - 20*C*a^11*b^4 + 12*C*a^12*b^3 + 12*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 4*B*a^2*b - 2*C*a*b^2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
808,1,9286,289,17.503077,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^5-2\,C\,b^5+6\,B\,a^2\,b^3+B\,a^3\,b^2+4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-2\,B\,a^4\,b+2\,C\,a\,b^4-3\,C\,a^4\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^5+2\,C\,b^5+6\,B\,a^2\,b^3-B\,a^3\,b^2-4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-2\,B\,a^4\,b+2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,C\,a^6-2\,B\,a^5\,b-13\,C\,a^4\,b^2+5\,B\,a^3\,b^3+6\,C\,a^2\,b^4-2\,C\,b^6\right)}{b\,\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(B\,b-3\,C\,a\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(B\,b-3\,C\,a\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(-4\,B^3\,a^9\,b^3+2\,B^3\,a^8\,b^4+18\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6-36\,B^3\,a^5\,b^7+26\,B^3\,a^4\,b^8+34\,B^3\,a^3\,b^9-24\,B^3\,a^2\,b^{10}-12\,B^3\,a\,b^{11}+36\,B^2\,C\,a^{10}\,b^2-18\,B^2\,C\,a^9\,b^3-162\,B^2\,C\,a^8\,b^4+105\,B^2\,C\,a^7\,b^5+312\,B^2\,C\,a^6\,b^6-198\,B^2\,C\,a^5\,b^7-282\,B^2\,C\,a^4\,b^8+156\,B^2\,C\,a^3\,b^9+96\,B^2\,C\,a^2\,b^{10}-108\,B\,C^2\,a^{11}\,b+54\,B\,C^2\,a^{10}\,b^2+486\,B\,C^2\,a^9\,b^3-279\,B\,C^2\,a^8\,b^4-900\,B\,C^2\,a^7\,b^5+486\,B\,C^2\,a^6\,b^6+774\,B\,C^2\,a^5\,b^7-324\,B\,C^2\,a^4\,b^8-252\,B\,C^2\,a^3\,b^9+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(B\,b-3\,C\,a\right)}{b^4}\right)}{b^4}+\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(B\,b-3\,C\,a\right)}{b^4}\right)}{b^4}}\right)\,\left(B\,b-3\,C\,a\right)\,2{}\mathrm{i}}{b^4\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(-4\,B^3\,a^9\,b^3+2\,B^3\,a^8\,b^4+18\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6-36\,B^3\,a^5\,b^7+26\,B^3\,a^4\,b^8+34\,B^3\,a^3\,b^9-24\,B^3\,a^2\,b^{10}-12\,B^3\,a\,b^{11}+36\,B^2\,C\,a^{10}\,b^2-18\,B^2\,C\,a^9\,b^3-162\,B^2\,C\,a^8\,b^4+105\,B^2\,C\,a^7\,b^5+312\,B^2\,C\,a^6\,b^6-198\,B^2\,C\,a^5\,b^7-282\,B^2\,C\,a^4\,b^8+156\,B^2\,C\,a^3\,b^9+96\,B^2\,C\,a^2\,b^{10}-108\,B\,C^2\,a^{11}\,b+54\,B\,C^2\,a^{10}\,b^2+486\,B\,C^2\,a^9\,b^3-279\,B\,C^2\,a^8\,b^4-900\,B\,C^2\,a^7\,b^5+486\,B\,C^2\,a^6\,b^6+774\,B\,C^2\,a^5\,b^7-324\,B\,C^2\,a^4\,b^8-252\,B\,C^2\,a^3\,b^9+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(6*C*a^5 - 2*C*b^5 + 6*B*a^2*b^3 + B*a^3*b^2 + 4*C*a^2*b^3 - 12*C*a^3*b^2 - 2*B*a^4*b + 2*C*a*b^4 - 3*C*a^4*b))/((a*b^3 - b^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(6*C*a^5 + 2*C*b^5 + 6*B*a^2*b^3 - B*a^3*b^2 - 4*C*a^2*b^3 - 12*C*a^3*b^2 - 2*B*a^4*b + 2*C*a*b^4 + 3*C*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) - (2*tan(c/2 + (d*x)/2)^3*(6*C*a^6 - 2*C*b^6 + 5*B*a^3*b^3 + 6*C*a^2*b^4 - 13*C*a^4*b^2 - 2*B*a^5*b))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) + (atan((((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(B*b - 3*C*a))/b^4)*1i)/b^4 + ((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(B*b - 3*C*a))/b^4)*1i)/b^4)/((16*(108*C^3*a^12 - 12*B^3*a*b^11 - 54*C^3*a^11*b - 24*B^3*a^2*b^10 + 34*B^3*a^3*b^9 + 26*B^3*a^4*b^8 - 36*B^3*a^5*b^7 - 13*B^3*a^6*b^6 + 18*B^3*a^7*b^5 + 2*B^3*a^8*b^4 - 4*B^3*a^9*b^3 + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 - 108*B*C^2*a^11*b - 252*B*C^2*a^3*b^9 - 324*B*C^2*a^4*b^8 + 774*B*C^2*a^5*b^7 + 486*B*C^2*a^6*b^6 - 900*B*C^2*a^7*b^5 - 279*B*C^2*a^8*b^4 + 486*B*C^2*a^9*b^3 + 54*B*C^2*a^10*b^2 + 96*B^2*C*a^2*b^10 + 156*B^2*C*a^3*b^9 - 282*B^2*C*a^4*b^8 - 198*B^2*C*a^5*b^7 + 312*B^2*C*a^6*b^6 + 105*B^2*C*a^7*b^5 - 162*B^2*C*a^8*b^4 - 18*B^2*C*a^9*b^3 + 36*B^2*C*a^10*b^2))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - ((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(B*b - 3*C*a))/b^4))/b^4 + ((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(B*b - 3*C*a))/b^4))/b^4))*(B*b - 3*C*a)*2i)/(b^4*d) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(108*C^3*a^12 - 12*B^3*a*b^11 - 54*C^3*a^11*b - 24*B^3*a^2*b^10 + 34*B^3*a^3*b^9 + 26*B^3*a^4*b^8 - 36*B^3*a^5*b^7 - 13*B^3*a^6*b^6 + 18*B^3*a^7*b^5 + 2*B^3*a^8*b^4 - 4*B^3*a^9*b^3 + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 - 108*B*C^2*a^11*b - 252*B*C^2*a^3*b^9 - 324*B*C^2*a^4*b^8 + 774*B*C^2*a^5*b^7 + 486*B*C^2*a^6*b^6 - 900*B*C^2*a^7*b^5 - 279*B*C^2*a^8*b^4 + 486*B*C^2*a^9*b^3 + 54*B*C^2*a^10*b^2 + 96*B^2*C*a^2*b^10 + 156*B^2*C*a^3*b^9 - 282*B^2*C*a^4*b^8 - 198*B^2*C*a^5*b^7 + 312*B^2*C*a^6*b^6 + 105*B^2*C*a^7*b^5 - 162*B^2*C*a^8*b^4 - 18*B^2*C*a^9*b^3 + 36*B^2*C*a^10*b^2))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - (a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*1i)/(d*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
809,1,6899,220,14.000318,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^4+B\,a^2\,b^2-6\,C\,a^2\,b^2+4\,B\,a\,b^3-C\,a^3\,b\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a^4-B\,a^2\,b^2-6\,C\,a^2\,b^2+4\,B\,a\,b^3+C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{C\,\mathrm{atan}\left(-\frac{\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)\,1{}\mathrm{i}}{b^3}-\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)}{b^3}+\frac{C\,\left(\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}\right)}{b^3}}\right)\,2{}\mathrm{i}}{b^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*C*a^4 + B*a^2*b^2 - 6*C*a^2*b^2 + 4*B*a*b^3 - C*a^3*b))/((a*b^2 - b^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*C*a^4 - B*a^2*b^2 - 6*C*a^2*b^2 + 4*B*a*b^3 + C*a^3*b))/((a + b)*(b^4 - 2*a*b^3 + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (C*atan(-((C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3 - (C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3)/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 - 20*B*C^2*a*b^8 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 + (C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3))*2i)/(b^3*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 - 20*B*C^2*a*b^8 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*1i)/(d*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
810,1,251,180,7.394360,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^3),x)","\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(C\,a^2-3\,B\,a\,b+2\,C\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,a^2+2\,B\,b^2-C\,a^2+B\,a\,b-4\,C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a^2+2\,B\,b^2+C\,a^2-B\,a\,b-4\,C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(atanh((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(C*a^2 + 2*C*b^2 - 3*B*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((tan(c/2 + (d*x)/2)^3*(2*B*a^2 + 2*B*b^2 - C*a^2 + B*a*b - 4*C*a*b))/((a + b)^2*(a - b)) - (tan(c/2 + (d*x)/2)*(2*B*a^2 + 2*B*b^2 + C*a^2 - B*a*b - 4*C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
811,1,251,164,7.263845,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^3,x)","\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,B\,a^2-3\,C\,a\,b+B\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^2-B\,b^2+2\,C\,b^2-4\,B\,a\,b+C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2+2\,C\,a^2+2\,C\,b^2-4\,B\,a\,b-C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(atanh((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*B*a^2 + B*b^2 - 3*C*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((tan(c/2 + (d*x)/2)^3*(2*C*a^2 - B*b^2 + 2*C*b^2 - 4*B*a*b + C*a*b))/((a + b)^2*(a - b)) - (tan(c/2 + (d*x)/2)*(B*b^2 + 2*C*a^2 + 2*C*b^2 - 4*B*a*b - C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
812,1,6911,205,15.431823,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b^4-6\,B\,a^2\,b^2+C\,a^2\,b^2-B\,a\,b^3+4\,C\,a^3\,b\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4-6\,B\,a^2\,b^2-C\,a^2\,b^2+B\,a\,b^3+4\,C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{2\,B\,\mathrm{atan}\left(-\frac{\frac{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)}{a^3}-\frac{B\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)}{a^3}}{-\frac{16\,\left(12\,B^3\,a^8\,b+24\,B^3\,a^7\,b^2-34\,B^3\,a^6\,b^3-26\,B^3\,a^5\,b^4+36\,B^3\,a^4\,b^5+13\,B^3\,a^3\,b^6-18\,B^3\,a^2\,b^7-2\,B^3\,a\,b^8+4\,B^3\,b^9-4\,B^2\,C\,a^9-20\,B^2\,C\,a^8\,b+6\,B^2\,C\,a^7\,b^2+2\,B^2\,C\,a^6\,b^3+2\,B^2\,C\,a^4\,b^5-2\,B^2\,C\,a^3\,b^6-2\,B^2\,C\,a^2\,b^7+4\,B\,C^2\,a^9+4\,B\,C^2\,a^7\,b^2+B\,C^2\,a^5\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{B\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}\right)}{a^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(12\,B^3\,a^8\,b+24\,B^3\,a^7\,b^2-34\,B^3\,a^6\,b^3-26\,B^3\,a^5\,b^4+36\,B^3\,a^4\,b^5+13\,B^3\,a^3\,b^6-18\,B^3\,a^2\,b^7-2\,B^3\,a\,b^8+4\,B^3\,b^9-4\,B^2\,C\,a^9-20\,B^2\,C\,a^8\,b+6\,B^2\,C\,a^7\,b^2+2\,B^2\,C\,a^6\,b^3+2\,B^2\,C\,a^4\,b^5-2\,B^2\,C\,a^3\,b^6-2\,B^2\,C\,a^2\,b^7+4\,B\,C^2\,a^9+4\,B\,C^2\,a^7\,b^2+B\,C^2\,a^5\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"(2*B*atan(-((B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 - (B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3)/((B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3 - (16*(4*B^3*b^9 + 4*B*C^2*a^9 - 4*B^2*C*a^9 - 2*B^3*a*b^8 + 12*B^3*a^8*b - 18*B^3*a^2*b^7 + 13*B^3*a^3*b^6 + 36*B^3*a^4*b^5 - 26*B^3*a^5*b^4 - 34*B^3*a^6*b^3 + 24*B^3*a^7*b^2 - 20*B^2*C*a^8*b + B*C^2*a^5*b^4 + 4*B*C^2*a^7*b^2 - 2*B^2*C*a^2*b^7 - 2*B^2*C*a^3*b^6 + 2*B^2*C*a^4*b^5 + 2*B^2*C*a^6*b^3 + 6*B^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3)))/(a^3*d) - ((tan(c/2 + (d*x)/2)^3*(2*B*b^4 - 6*B*a^2*b^2 + C*a^2*b^2 - B*a*b^3 + 4*C*a^3*b))/((a^2*b - a^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*b^4 - 6*B*a^2*b^2 - C*a^2*b^2 + B*a*b^3 + 4*C*a^3*b))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(4*B^3*b^9 + 4*B*C^2*a^9 - 4*B^2*C*a^9 - 2*B^3*a*b^8 + 12*B^3*a^8*b - 18*B^3*a^2*b^7 + 13*B^3*a^3*b^6 + 36*B^3*a^4*b^5 - 26*B^3*a^5*b^4 - 34*B^3*a^6*b^3 + 24*B^3*a^7*b^2 - 20*B^2*C*a^8*b + B*C^2*a^5*b^4 + 4*B*C^2*a^7*b^2 - 2*B^2*C*a^2*b^7 - 2*B^2*C*a^3*b^6 + 2*B^2*C*a^4*b^5 + 2*B^2*C*a^6*b^3 + 6*B^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
813,1,5530,290,12.586588,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,B\,b^5-2\,B\,a^5-12\,B\,a^2\,b^3+4\,B\,a^3\,b^2+C\,a^2\,b^3+6\,C\,a^3\,b^2-3\,B\,a\,b^4+2\,B\,a^4\,b-2\,C\,a\,b^4\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a^5+6\,B\,b^5-12\,B\,a^2\,b^3-4\,B\,a^3\,b^2-C\,a^2\,b^3+6\,C\,a^3\,b^2+3\,B\,a\,b^4+2\,B\,a^4\,b-2\,C\,a\,b^4\right)}{\left(a+b\right)\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,a^6-6\,B\,a^4\,b^2-5\,C\,a^3\,b^3+13\,B\,a^2\,b^4+2\,C\,a\,b^5-6\,B\,b^6\right)}{a\,\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(3\,B\,b-C\,a\right)\,1{}\mathrm{i}}{a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b\,3{}\mathrm{i}-C\,a\,1{}\mathrm{i}\right)}{a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{16\,\left(216\,B^3\,a^8\,b^4+216\,B^3\,a^7\,b^5-702\,B^3\,a^6\,b^6-378\,B^3\,a^5\,b^7+864\,B^3\,a^4\,b^8+243\,B^3\,a^3\,b^9-486\,B^3\,a^2\,b^{10}-54\,B^3\,a\,b^{11}+108\,B^3\,b^{12}-252\,B^2\,C\,a^9\,b^3-324\,B^2\,C\,a^8\,b^4+774\,B^2\,C\,a^7\,b^5+486\,B^2\,C\,a^6\,b^6-900\,B^2\,C\,a^5\,b^7-279\,B^2\,C\,a^4\,b^8+486\,B^2\,C\,a^3\,b^9+54\,B^2\,C\,a^2\,b^{10}-108\,B^2\,C\,a\,b^{11}+96\,B\,C^2\,a^{10}\,b^2+156\,B\,C^2\,a^9\,b^3-282\,B\,C^2\,a^8\,b^4-198\,B\,C^2\,a^7\,b^5+312\,B\,C^2\,a^6\,b^6+105\,B\,C^2\,a^5\,b^7-162\,B\,C^2\,a^4\,b^8-18\,B\,C^2\,a^3\,b^9+36\,B\,C^2\,a^2\,b^{10}-12\,C^3\,a^{11}\,b-24\,C^3\,a^{10}\,b^2+34\,C^3\,a^9\,b^3+26\,C^3\,a^8\,b^4-36\,C^3\,a^7\,b^5-13\,C^3\,a^6\,b^6+18\,C^3\,a^5\,b^7+2\,C^3\,a^4\,b^8-4\,C^3\,a^3\,b^9\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(6*B*b^5 - 2*B*a^5 - 12*B*a^2*b^3 + 4*B*a^3*b^2 + C*a^2*b^3 + 6*C*a^3*b^2 - 3*B*a*b^4 + 2*B*a^4*b - 2*C*a*b^4))/((a^3*b - a^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*a^5 + 6*B*b^5 - 12*B*a^2*b^3 - 4*B*a^3*b^2 - C*a^2*b^3 + 6*C*a^3*b^2 + 3*B*a*b^4 + 2*B*a^4*b - 2*C*a*b^4))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(2*B*a^6 - 6*B*b^6 + 13*B*a^2*b^4 - 6*B*a^4*b^2 - 5*C*a^3*b^3 + 2*C*a*b^5))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) + (log(tan(c/2 + (d*x)/2) - 1i)*(3*B*b - C*a)*1i)/(a^4*d) - (log(tan(c/2 + (d*x)/2) + 1i)*(B*b*3i - C*a*1i))/(a^4*d) - (b*atan(((b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((16*(108*B^3*b^12 - 54*B^3*a*b^11 - 12*C^3*a^11*b - 486*B^3*a^2*b^10 + 243*B^3*a^3*b^9 + 864*B^3*a^4*b^8 - 378*B^3*a^5*b^7 - 702*B^3*a^6*b^6 + 216*B^3*a^7*b^5 + 216*B^3*a^8*b^4 - 4*C^3*a^3*b^9 + 2*C^3*a^4*b^8 + 18*C^3*a^5*b^7 - 13*C^3*a^6*b^6 - 36*C^3*a^7*b^5 + 26*C^3*a^8*b^4 + 34*C^3*a^9*b^3 - 24*C^3*a^10*b^2 - 108*B^2*C*a*b^11 + 36*B*C^2*a^2*b^10 - 18*B*C^2*a^3*b^9 - 162*B*C^2*a^4*b^8 + 105*B*C^2*a^5*b^7 + 312*B*C^2*a^6*b^6 - 198*B*C^2*a^7*b^5 - 282*B*C^2*a^8*b^4 + 156*B*C^2*a^9*b^3 + 96*B*C^2*a^10*b^2 + 54*B^2*C*a^2*b^10 + 486*B^2*C*a^3*b^9 - 279*B^2*C*a^4*b^8 - 900*B^2*C*a^5*b^7 + 486*B^2*C*a^6*b^6 + 774*B^2*C*a^7*b^5 - 324*B^2*C*a^8*b^4 - 252*B^2*C*a^9*b^3))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - (b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*1i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
814,0,-1,485,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
815,0,-1,397,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
816,0,-1,314,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
817,0,-1,256,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int \left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
818,0,-1,320,0.000000,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
819,0,-1,344,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
820,0,-1,429,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/2), x)","F"
821,0,-1,573,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
822,0,-1,475,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
823,0,-1,387,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
824,0,-1,312,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int \left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
825,0,-1,380,0.000000,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
826,0,-1,361,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
827,0,-1,428,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
828,0,-1,520,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(3/2), x)","F"
829,0,-1,565,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
830,0,-1,469,0.000000,"\text{Not used}","int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
831,0,-1,384,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int \left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
832,0,-1,442,0.000000,"\text{Not used}","int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
833,0,-1,433,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
834,0,-1,450,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
835,0,-1,518,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^4*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
836,0,-1,617,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^5*(B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(5/2), x)","F"
837,0,-1,411,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)), x)","F"
838,0,-1,329,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)), x)","F"
839,0,-1,261,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)), x)","F"
840,0,-1,210,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2), x)","F"
841,0,-1,208,0.000000,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
842,0,-1,348,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
843,0,-1,471,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)), x)","F"
844,0,-1,329,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)), x)","F"
845,0,-1,275,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)), x)","F"
846,0,-1,254,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2), x)","F"
847,0,-1,376,0.000000,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
848,0,-1,427,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
849,0,-1,509,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)), x)","F"
850,0,-1,417,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)), x)","F"
851,0,-1,387,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)), x)","F"
852,0,-1,353,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2), x)","F"
853,0,-1,495,0.000000,"\text{Not used}","int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
854,0,-1,446,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(7/2),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(7/2), x)","F"
855,0,-1,101,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
856,0,-1,138,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
857,0,-1,229,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(2/3),x)","\int \left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(2/3), x)","F"
858,0,-1,229,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/3),x)","\int \left(\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)*(a + b/cos(c + d*x))^(1/3), x)","F"
859,0,-1,226,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/3),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/3), x)","F"
860,0,-1,226,0.000000,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(2/3),x)","\int \frac{\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(2/3), x)","F"
861,1,301,165,7.670613,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A\,a}{2}+\frac{3\,B\,b}{8}+\frac{3\,C\,a}{8}\right)}{2\,A\,a+\frac{3\,B\,b}{2}+\frac{3\,C\,a}{2}}\right)\,\left(A\,a+\frac{3\,B\,b}{4}+\frac{3\,C\,a}{4}\right)}{d}-\frac{\left(2\,A\,b-A\,a+2\,B\,a-\frac{5\,B\,b}{4}-\frac{5\,C\,a}{4}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,a-\frac{16\,A\,b}{3}-\frac{16\,B\,a}{3}+\frac{B\,b}{2}+\frac{C\,a}{2}-\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b}{3}+\frac{20\,B\,a}{3}+\frac{116\,C\,b}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-2\,A\,a-\frac{16\,A\,b}{3}-\frac{16\,B\,a}{3}-\frac{B\,b}{2}-\frac{C\,a}{2}-\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a+2\,A\,b+2\,B\,a+\frac{5\,B\,b}{4}+\frac{5\,C\,a}{4}+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((A*a)/2 + (3*B*b)/8 + (3*C*a)/8))/(2*A*a + (3*B*b)/2 + (3*C*a)/2))*(A*a + (3*B*b)/4 + (3*C*a)/4))/d - (tan(c/2 + (d*x)/2)^7*(2*A*a - (16*A*b)/3 - (16*B*a)/3 + (B*b)/2 + (C*a)/2 - (8*C*b)/3) - tan(c/2 + (d*x)/2)^3*(2*A*a + (16*A*b)/3 + (16*B*a)/3 + (B*b)/2 + (C*a)/2 + (8*C*b)/3) - tan(c/2 + (d*x)/2)^9*(A*a - 2*A*b - 2*B*a + (5*B*b)/4 + (5*C*a)/4 - 2*C*b) + tan(c/2 + (d*x)/2)*(A*a + 2*A*b + 2*B*a + (5*B*b)/4 + (5*C*a)/4 + 2*C*b) + tan(c/2 + (d*x)/2)^5*((20*A*b)/3 + (20*B*a)/3 + (116*C*b)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
862,1,260,137,7.719920,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A\,b}{2}+\frac{B\,a}{2}+\frac{3\,C\,b}{8}\right)}{2\,A\,b+2\,B\,a+\frac{3\,C\,b}{2}}\right)\,\left(A\,b+B\,a+\frac{3\,C\,b}{4}\right)}{d}-\frac{\left(2\,A\,a-A\,b-B\,a+2\,B\,b+2\,C\,a-\frac{5\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(A\,b-6\,A\,a+B\,a-\frac{10\,B\,b}{3}-\frac{10\,C\,a}{3}-\frac{3\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,a+A\,b+B\,a+\frac{10\,B\,b}{3}+\frac{10\,C\,a}{3}-\frac{3\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,A\,a-A\,b-B\,a-2\,B\,b-2\,C\,a-\frac{5\,C\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((A*b)/2 + (B*a)/2 + (3*C*b)/8))/(2*A*b + 2*B*a + (3*C*b)/2))*(A*b + B*a + (3*C*b)/4))/d - (tan(c/2 + (d*x)/2)^7*(2*A*a - A*b - B*a + 2*B*b + 2*C*a - (5*C*b)/4) + tan(c/2 + (d*x)/2)^3*(6*A*a + A*b + B*a + (10*B*b)/3 + (10*C*a)/3 - (3*C*b)/4) - tan(c/2 + (d*x)/2)^5*(6*A*a - A*b - B*a + (10*B*b)/3 + (10*C*a)/3 + (3*C*b)/4) - tan(c/2 + (d*x)/2)*(2*A*a + A*b + B*a + 2*B*b + 2*C*a + (5*C*b)/4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
863,1,190,101,7.655943,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a+\frac{B\,b}{2}+\frac{C\,a}{2}\right)}{4\,A\,a+2\,B\,b+2\,C\,a}\right)\,\left(2\,A\,a+B\,b+C\,a\right)}{d}-\frac{\left(2\,A\,b+2\,B\,a-B\,b-C\,a+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,b-4\,B\,a-\frac{4\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b+2\,B\,a+B\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*(A*a + (B*b)/2 + (C*a)/2))/(4*A*a + 2*B*b + 2*C*a))*(2*A*a + B*b + C*a))/d - (tan(c/2 + (d*x)/2)^5*(2*A*b + 2*B*a - B*b - C*a + 2*C*b) + tan(c/2 + (d*x)/2)*(2*A*b + 2*B*a + B*b + C*a + 2*C*b) - tan(c/2 + (d*x)/2)^3*(4*A*b + 4*B*a + (4*C*b)/3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
864,1,164,69,4.587728,"\text{Not used}","int((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+A\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}\right)}{d}+\frac{\frac{C\,b\,\sin\left(c+d\,x\right)}{2}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + A*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2))/d + ((C*b*sin(c + d*x))/2 + (B*b*sin(2*c + 2*d*x))/2 + (C*a*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
865,1,153,52,4.260314,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{C\,b\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,A\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*b*tan(c + d*x))/d + (2*A*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(2*c + 2*d*x))/(2*d*cos(c + d*x))","B"
866,1,156,69,4.105893,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{A\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*b*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(2*c + 2*d*x))/(4*d)","B"
867,1,100,92,4.039770,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{A\,b\,x}{2}+\frac{B\,a\,x}{2}+C\,b\,x+\frac{3\,A\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{A\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*b*x)/2 + (B*a*x)/2 + C*b*x + (3*A*a*sin(c + d*x))/(4*d) + (B*b*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (A*a*sin(3*c + 3*d*x))/(12*d) + (A*b*sin(2*c + 2*d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d)","B"
868,1,150,116,3.898877,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{3\,A\,a\,x}{8}+\frac{B\,b\,x}{2}+\frac{C\,a\,x}{2}+\frac{3\,A\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,B\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{A\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(3*A*a*x)/8 + (B*b*x)/2 + (C*a*x)/2 + (3*A*b*sin(c + d*x))/(4*d) + (3*B*a*sin(c + d*x))/(4*d) + (C*b*sin(c + d*x))/d + (A*a*sin(2*c + 2*d*x))/(4*d) + (A*a*sin(4*c + 4*d*x))/(32*d) + (A*b*sin(3*c + 3*d*x))/(12*d) + (B*a*sin(3*c + 3*d*x))/(12*d) + (B*b*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d)","B"
869,1,258,156,7.629093,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{x\,\left(\frac{3\,A\,b}{4}+\frac{3\,B\,a}{4}+C\,b\right)}{2}+\frac{\left(2\,A\,a-\frac{5\,A\,b}{4}-\frac{5\,B\,a}{4}+2\,B\,b+2\,C\,a-C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a}{3}-\frac{A\,b}{2}-\frac{B\,a}{2}+\frac{16\,B\,b}{3}+\frac{16\,C\,a}{3}-2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,B\,b}{3}+\frac{20\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a}{3}+\frac{A\,b}{2}+\frac{B\,a}{2}+\frac{16\,B\,b}{3}+\frac{16\,C\,a}{3}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+\frac{5\,A\,b}{4}+\frac{5\,B\,a}{4}+2\,B\,b+2\,C\,a+C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*((3*A*b)/4 + (3*B*a)/4 + C*b))/2 + (tan(c/2 + (d*x)/2)^9*(2*A*a - (5*A*b)/4 - (5*B*a)/4 + 2*B*b + 2*C*a - C*b) + tan(c/2 + (d*x)/2)^3*((8*A*a)/3 + (A*b)/2 + (B*a)/2 + (16*B*b)/3 + (16*C*a)/3 + 2*C*b) + tan(c/2 + (d*x)/2)^7*((8*A*a)/3 - (A*b)/2 - (B*a)/2 + (16*B*b)/3 + (16*C*a)/3 - 2*C*b) + tan(c/2 + (d*x)/2)*(2*A*a + (5*A*b)/4 + (5*B*a)/4 + 2*B*b + 2*C*a + C*b) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*B*b)/3 + (20*C*a)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1))","B"
870,1,455,233,7.476727,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,a^2}{2}+\frac{3\,B\,b^2}{8}+A\,a\,b+\frac{3\,C\,a\,b}{4}\right)}{2\,B\,a^2+\frac{3\,B\,b^2}{2}+4\,A\,a\,b+3\,C\,a\,b}\right)\,\left(B\,a^2+\frac{3\,B\,b^2}{4}+2\,A\,a\,b+\frac{3\,C\,a\,b}{2}\right)}{d}-\frac{\left(2\,A\,a^2+2\,A\,b^2-B\,a^2-\frac{5\,B\,b^2}{4}+2\,C\,a^2+2\,C\,b^2-2\,A\,a\,b+4\,B\,a\,b-\frac{5\,C\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,B\,a^2-\frac{16\,A\,b^2}{3}-8\,A\,a^2+\frac{B\,b^2}{2}-\frac{16\,C\,a^2}{3}-\frac{8\,C\,b^2}{3}+4\,A\,a\,b-\frac{32\,B\,a\,b}{3}+C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,A\,a^2+\frac{20\,A\,b^2}{3}+\frac{20\,C\,a^2}{3}+\frac{116\,C\,b^2}{15}+\frac{40\,B\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,A\,a^2-\frac{16\,A\,b^2}{3}-2\,B\,a^2-\frac{B\,b^2}{2}-\frac{16\,C\,a^2}{3}-\frac{8\,C\,b^2}{3}-4\,A\,a\,b-\frac{32\,B\,a\,b}{3}-C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+B\,a^2+\frac{5\,B\,b^2}{4}+2\,C\,a^2+2\,C\,b^2+2\,A\,a\,b+4\,B\,a\,b+\frac{5\,C\,a\,b}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((B*a^2)/2 + (3*B*b^2)/8 + A*a*b + (3*C*a*b)/4))/(2*B*a^2 + (3*B*b^2)/2 + 4*A*a*b + 3*C*a*b))*(B*a^2 + (3*B*b^2)/4 + 2*A*a*b + (3*C*a*b)/2))/d - (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 + (5*B*b^2)/4 + 2*C*a^2 + 2*C*b^2 + 2*A*a*b + 4*B*a*b + (5*C*a*b)/2) + tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 - B*a^2 - (5*B*b^2)/4 + 2*C*a^2 + 2*C*b^2 - 2*A*a*b + 4*B*a*b - (5*C*a*b)/2) - tan(c/2 + (d*x)/2)^3*(8*A*a^2 + (16*A*b^2)/3 + 2*B*a^2 + (B*b^2)/2 + (16*C*a^2)/3 + (8*C*b^2)/3 + 4*A*a*b + (32*B*a*b)/3 + C*a*b) - tan(c/2 + (d*x)/2)^7*(8*A*a^2 + (16*A*b^2)/3 - 2*B*a^2 - (B*b^2)/2 + (16*C*a^2)/3 + (8*C*b^2)/3 - 4*A*a*b + (32*B*a*b)/3 - C*a*b) + tan(c/2 + (d*x)/2)^5*(12*A*a^2 + (20*A*b^2)/3 + (20*C*a^2)/3 + (116*C*b^2)/15 + (40*B*a*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
871,1,389,200,8.189914,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\left(A\,b^2-2\,B\,a^2-2\,B\,b^2+C\,a^2+\frac{5\,C\,b^2}{4}-4\,A\,a\,b+2\,B\,a\,b-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,B\,a^2-A\,b^2+\frac{10\,B\,b^2}{3}-C\,a^2+\frac{3\,C\,b^2}{4}+12\,A\,a\,b-2\,B\,a\,b+\frac{20\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,C\,b^2}{4}-6\,B\,a^2-\frac{10\,B\,b^2}{3}-C\,a^2-A\,b^2-12\,A\,a\,b-2\,B\,a\,b-\frac{20\,C\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,b^2+2\,B\,a^2+2\,B\,b^2+C\,a^2+\frac{5\,C\,b^2}{4}+4\,A\,a\,b+2\,B\,a\,b+4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2+\frac{A\,b^2}{2}+\frac{C\,a^2}{2}+\frac{3\,C\,b^2}{8}+B\,a\,b\right)}{4\,A\,a^2+2\,A\,b^2+2\,C\,a^2+\frac{3\,C\,b^2}{2}+4\,B\,a\,b}\right)\,\left(2\,A\,a^2+A\,b^2+C\,a^2+\frac{3\,C\,b^2}{4}+2\,B\,a\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(A*b^2 - 2*B*a^2 - 2*B*b^2 + C*a^2 + (5*C*b^2)/4 - 4*A*a*b + 2*B*a*b - 4*C*a*b) - tan(c/2 + (d*x)/2)^3*(A*b^2 + 6*B*a^2 + (10*B*b^2)/3 + C*a^2 - (3*C*b^2)/4 + 12*A*a*b + 2*B*a*b + (20*C*a*b)/3) + tan(c/2 + (d*x)/2)^5*(6*B*a^2 - A*b^2 + (10*B*b^2)/3 - C*a^2 + (3*C*b^2)/4 + 12*A*a*b - 2*B*a*b + (20*C*a*b)/3) + tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 + C*a^2 + (5*C*b^2)/4 + 4*A*a*b + 2*B*a*b + 4*C*a*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*(A*a^2 + (A*b^2)/2 + (C*a^2)/2 + (3*C*b^2)/8 + B*a*b))/(4*A*a^2 + 2*A*b^2 + 2*C*a^2 + (3*C*b^2)/2 + 4*B*a*b))*(2*A*a^2 + A*b^2 + C*a^2 + (3*C*b^2)/4 + 2*B*a*b))/d","B"
872,1,512,134,5.910398,"\text{Not used}","int((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{A\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{A\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{2}+\frac{B\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,A\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{3\,B\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{3\,B\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{B\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,a\,b\,\sin\left(c+d\,x\right)}{2}+3\,A\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{3\,C\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+A\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+\frac{C\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*b^2*sin(3*c + 3*d*x))/4 + (B*b^2*sin(2*c + 2*d*x))/4 + (C*a^2*sin(3*c + 3*d*x))/4 + (C*b^2*sin(3*c + 3*d*x))/6 + (A*b^2*sin(c + d*x))/4 + (C*a^2*sin(c + d*x))/4 + (C*b^2*sin(c + d*x))/2 + (B*a*b*sin(3*c + 3*d*x))/2 + (C*a*b*sin(2*c + 2*d*x))/2 + (3*A*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (3*B*a^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (3*B*b^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (B*a*b*sin(c + d*x))/2 + 3*A*a*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (3*C*a*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + A*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + (C*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
873,1,257,126,6.154881,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+2\,A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,B\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{2}+C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + A*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 2*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*B*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((A*a^2*sin(3*c + 3*d*x))/4 + (B*b^2*sin(2*c + 2*d*x))/2 + (A*a^2*sin(c + d*x))/4 + (C*b^2*sin(c + d*x))/2 + C*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
874,1,274,118,4.639568,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}-\frac{A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{B\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}-\frac{C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}","Not used",1,"(B*a^2*sin(c + d*x))/d - (A*a^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d - (A*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (B*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (C*b^2*sin(c + d*x))/(d*cos(c + d*x)) + (2*A*a*b*sin(c + d*x))/d - (B*a*b*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d - (C*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (A*a^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
875,1,263,141,4.554265,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{3\,A\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,B\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(3*A*a^2*sin(c + d*x))/(4*d) + (A*b^2*sin(c + d*x))/d + (C*a^2*sin(c + d*x))/d + (B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^2*sin(3*c + 3*d*x))/(12*d) + (B*a^2*sin(2*c + 2*d*x))/(4*d) + (2*B*a*b*sin(c + d*x))/d + (2*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*b*sin(2*c + 2*d*x))/(2*d)","B"
876,1,214,175,4.129797,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{3\,A\,a^2\,x}{8}+\frac{A\,b^2\,x}{2}+\frac{C\,a^2\,x}{2}+C\,b^2\,x+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b^2\,\sin\left(c+d\,x\right)}{d}+B\,a\,b\,x+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,A\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{2\,C\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{B\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(3*A*a^2*x)/8 + (A*b^2*x)/2 + (C*a^2*x)/2 + C*b^2*x + (3*B*a^2*sin(c + d*x))/(4*d) + (B*b^2*sin(c + d*x))/d + B*a*b*x + (A*a^2*sin(2*c + 2*d*x))/(4*d) + (A*a^2*sin(4*c + 4*d*x))/(32*d) + (A*b^2*sin(2*c + 2*d*x))/(4*d) + (B*a^2*sin(3*c + 3*d*x))/(12*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (3*A*a*b*sin(c + d*x))/(2*d) + (2*C*a*b*sin(c + d*x))/d + (A*a*b*sin(3*c + 3*d*x))/(6*d) + (B*a*b*sin(2*c + 2*d*x))/(2*d)","B"
877,1,256,215,4.549545,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\frac{25\,A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,A\,a^2\,\sin\left(5\,c+5\,d\,x\right)}{2}+30\,B\,a^2\,\sin\left(2\,c+2\,d\,x\right)+10\,A\,b^2\,\sin\left(3\,c+3\,d\,x\right)+\frac{15\,B\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{4}+30\,B\,b^2\,\sin\left(2\,c+2\,d\,x\right)+10\,C\,a^2\,\sin\left(3\,c+3\,d\,x\right)+75\,A\,a^2\,\sin\left(c+d\,x\right)+90\,A\,b^2\,\sin\left(c+d\,x\right)+90\,C\,a^2\,\sin\left(c+d\,x\right)+120\,C\,b^2\,\sin\left(c+d\,x\right)+60\,A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)+\frac{15\,A\,a\,b\,\sin\left(4\,c+4\,d\,x\right)}{2}+20\,B\,a\,b\,\sin\left(3\,c+3\,d\,x\right)+60\,C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)+45\,B\,a^2\,d\,x+60\,B\,b^2\,d\,x+180\,B\,a\,b\,\sin\left(c+d\,x\right)+90\,A\,a\,b\,d\,x+120\,C\,a\,b\,d\,x}{120\,d}","Not used",1,"((25*A*a^2*sin(3*c + 3*d*x))/2 + (3*A*a^2*sin(5*c + 5*d*x))/2 + 30*B*a^2*sin(2*c + 2*d*x) + 10*A*b^2*sin(3*c + 3*d*x) + (15*B*a^2*sin(4*c + 4*d*x))/4 + 30*B*b^2*sin(2*c + 2*d*x) + 10*C*a^2*sin(3*c + 3*d*x) + 75*A*a^2*sin(c + d*x) + 90*A*b^2*sin(c + d*x) + 90*C*a^2*sin(c + d*x) + 120*C*b^2*sin(c + d*x) + 60*A*a*b*sin(2*c + 2*d*x) + (15*A*a*b*sin(4*c + 4*d*x))/2 + 20*B*a*b*sin(3*c + 3*d*x) + 60*C*a*b*sin(2*c + 2*d*x) + 45*B*a^2*d*x + 60*B*b^2*d*x + 180*B*a*b*sin(c + d*x) + 90*A*a*b*d*x + 120*C*a*b*d*x)/(120*d)","B"
878,1,769,381,6.246521,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A\,b^3}{8}+\frac{B\,a^3}{2}+\frac{5\,C\,b^3}{16}+\frac{3\,A\,a^2\,b}{2}+\frac{9\,B\,a\,b^2}{8}+\frac{9\,C\,a^2\,b}{8}\right)}{\frac{3\,A\,b^3}{2}+2\,B\,a^3+\frac{5\,C\,b^3}{4}+6\,A\,a^2\,b+\frac{9\,B\,a\,b^2}{2}+\frac{9\,C\,a^2\,b}{2}}\right)\,\left(\frac{3\,A\,b^3}{4}+B\,a^3+\frac{5\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{9\,B\,a\,b^2}{4}+\frac{9\,C\,a^2\,b}{4}\right)}{d}+\frac{\left(\frac{5\,A\,b^3}{4}-2\,A\,a^3+B\,a^3-2\,B\,b^3-2\,C\,a^3+\frac{11\,C\,b^3}{8}-6\,A\,a\,b^2+3\,A\,a^2\,b+\frac{15\,B\,a\,b^2}{4}-6\,B\,a^2\,b-6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(10\,A\,a^3-\frac{7\,A\,b^3}{4}-3\,B\,a^3+\frac{14\,B\,b^3}{3}+\frac{22\,C\,a^3}{3}+\frac{5\,C\,b^3}{24}+22\,A\,a\,b^2-9\,A\,a^2\,b-\frac{21\,B\,a\,b^2}{4}+22\,B\,a^2\,b+14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b^3}{2}-20\,A\,a^3+2\,B\,a^3-\frac{52\,B\,b^3}{5}-12\,C\,a^3+\frac{15\,C\,b^3}{4}-36\,A\,a\,b^2+6\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}-36\,B\,a^2\,b-\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(20\,A\,a^3+\frac{A\,b^3}{2}+2\,B\,a^3+\frac{52\,B\,b^3}{5}+12\,C\,a^3+\frac{15\,C\,b^3}{4}+36\,A\,a\,b^2+6\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+36\,B\,a^2\,b+\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,C\,b^3}{24}-\frac{7\,A\,b^3}{4}-3\,B\,a^3-\frac{14\,B\,b^3}{3}-\frac{22\,C\,a^3}{3}-10\,A\,a^3-22\,A\,a\,b^2-9\,A\,a^2\,b-\frac{21\,B\,a\,b^2}{4}-22\,B\,a^2\,b-14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+\frac{5\,A\,b^3}{4}+B\,a^3+2\,B\,b^3+2\,C\,a^3+\frac{11\,C\,b^3}{8}+6\,A\,a\,b^2+3\,A\,a^2\,b+\frac{15\,B\,a\,b^2}{4}+6\,B\,a^2\,b+6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*A*b^3)/8 + (B*a^3)/2 + (5*C*b^3)/16 + (3*A*a^2*b)/2 + (9*B*a*b^2)/8 + (9*C*a^2*b)/8))/((3*A*b^3)/2 + 2*B*a^3 + (5*C*b^3)/4 + 6*A*a^2*b + (9*B*a*b^2)/2 + (9*C*a^2*b)/2))*((3*A*b^3)/4 + B*a^3 + (5*C*b^3)/8 + 3*A*a^2*b + (9*B*a*b^2)/4 + (9*C*a^2*b)/4))/d + (tan(c/2 + (d*x)/2)*(2*A*a^3 + (5*A*b^3)/4 + B*a^3 + 2*B*b^3 + 2*C*a^3 + (11*C*b^3)/8 + 6*A*a*b^2 + 3*A*a^2*b + (15*B*a*b^2)/4 + 6*B*a^2*b + 6*C*a*b^2 + (15*C*a^2*b)/4) - tan(c/2 + (d*x)/2)^11*(2*A*a^3 - (5*A*b^3)/4 - B*a^3 + 2*B*b^3 + 2*C*a^3 - (11*C*b^3)/8 + 6*A*a*b^2 - 3*A*a^2*b - (15*B*a*b^2)/4 + 6*B*a^2*b + 6*C*a*b^2 - (15*C*a^2*b)/4) - tan(c/2 + (d*x)/2)^3*(10*A*a^3 + (7*A*b^3)/4 + 3*B*a^3 + (14*B*b^3)/3 + (22*C*a^3)/3 - (5*C*b^3)/24 + 22*A*a*b^2 + 9*A*a^2*b + (21*B*a*b^2)/4 + 22*B*a^2*b + 14*C*a*b^2 + (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^9*(10*A*a^3 - (7*A*b^3)/4 - 3*B*a^3 + (14*B*b^3)/3 + (22*C*a^3)/3 + (5*C*b^3)/24 + 22*A*a*b^2 - 9*A*a^2*b - (21*B*a*b^2)/4 + 22*B*a^2*b + 14*C*a*b^2 - (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^5*(20*A*a^3 + (A*b^3)/2 + 2*B*a^3 + (52*B*b^3)/5 + 12*C*a^3 + (15*C*b^3)/4 + 36*A*a*b^2 + 6*A*a^2*b + (3*B*a*b^2)/2 + 36*B*a^2*b + (156*C*a*b^2)/5 + (3*C*a^2*b)/2) - tan(c/2 + (d*x)/2)^7*(20*A*a^3 - (A*b^3)/2 - 2*B*a^3 + (52*B*b^3)/5 + 12*C*a^3 - (15*C*b^3)/4 + 36*A*a*b^2 - 6*A*a^2*b - (3*B*a*b^2)/2 + 36*B*a^2*b + (156*C*a*b^2)/5 - (3*C*a^2*b)/2))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
879,1,601,286,6.742332,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^3+\frac{3\,B\,b^3}{8}+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+\frac{9\,C\,a\,b^2}{8}\right)}{4\,A\,a^3+\frac{3\,B\,b^3}{2}+2\,C\,a^3+6\,A\,a\,b^2+6\,B\,a^2\,b+\frac{9\,C\,a\,b^2}{2}}\right)\,\left(2\,A\,a^3+\frac{3\,B\,b^3}{4}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b+\frac{9\,C\,a\,b^2}{4}\right)}{d}-\frac{\left(2\,A\,b^3+2\,B\,a^3-\frac{5\,B\,b^3}{4}-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,a^2\,b-\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B\,b^3}{2}-8\,B\,a^3-\frac{16\,A\,b^3}{3}+2\,C\,a^3-\frac{8\,C\,b^3}{3}+6\,A\,a\,b^2-24\,A\,a^2\,b-16\,B\,a\,b^2+6\,B\,a^2\,b+\frac{3\,C\,a\,b^2}{2}-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b^3}{3}+12\,B\,a^3+\frac{116\,C\,b^3}{15}+36\,A\,a^2\,b+20\,B\,a\,b^2+20\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,A\,b^3}{3}-8\,B\,a^3-\frac{B\,b^3}{2}-2\,C\,a^3-\frac{8\,C\,b^3}{3}-6\,A\,a\,b^2-24\,A\,a^2\,b-16\,B\,a\,b^2-6\,B\,a^2\,b-\frac{3\,C\,a\,b^2}{2}-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b^3+2\,B\,a^3+\frac{5\,B\,b^3}{4}+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2+3\,B\,a^2\,b+\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*(A*a^3 + (3*B*b^3)/8 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + (9*C*a*b^2)/8))/(4*A*a^3 + (3*B*b^3)/2 + 2*C*a^3 + 6*A*a*b^2 + 6*B*a^2*b + (9*C*a*b^2)/2))*(2*A*a^3 + (3*B*b^3)/4 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b + (9*C*a*b^2)/4))/d - (tan(c/2 + (d*x)/2)*(2*A*b^3 + 2*B*a^3 + (5*B*b^3)/4 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 + 3*B*a^2*b + (15*C*a*b^2)/4 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((20*A*b^3)/3 + 12*B*a^3 + (116*C*b^3)/15 + 36*A*a^2*b + 20*B*a*b^2 + 20*C*a^2*b) + tan(c/2 + (d*x)/2)^9*(2*A*b^3 + 2*B*a^3 - (5*B*b^3)/4 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 - 3*B*a^2*b - (15*C*a*b^2)/4 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((16*A*b^3)/3 + 8*B*a^3 + (B*b^3)/2 + 2*C*a^3 + (8*C*b^3)/3 + 6*A*a*b^2 + 24*A*a^2*b + 16*B*a*b^2 + 6*B*a^2*b + (3*C*a*b^2)/2 + 16*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((16*A*b^3)/3 + 8*B*a^3 - (B*b^3)/2 - 2*C*a^3 + (8*C*b^3)/3 - 6*A*a*b^2 + 24*A*a^2*b + 16*B*a*b^2 - 6*B*a^2*b - (3*C*a*b^2)/2 + 16*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
880,1,3210,207,6.906179,"\text{Not used}","int((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","-\frac{\left(2\,B\,b^3-A\,b^3+2\,C\,a^3-\frac{5\,C\,b^3}{4}+6\,A\,a\,b^2-3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(A\,b^3-\frac{10\,B\,b^3}{3}-6\,C\,a^3-\frac{3\,C\,b^3}{4}-18\,A\,a\,b^2+3\,B\,a\,b^2-18\,B\,a^2\,b-10\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(A\,b^3+\frac{10\,B\,b^3}{3}+6\,C\,a^3-\frac{3\,C\,b^3}{4}+18\,A\,a\,b^2+3\,B\,a\,b^2+18\,B\,a^2\,b+10\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-A\,b^3-2\,B\,b^3-2\,C\,a^3-\frac{5\,C\,b^3}{4}-6\,A\,a\,b^2-3\,B\,a\,b^2-6\,B\,a^2\,b-6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)\,1{}\mathrm{i}}{64\,A\,B^2\,a^9-\left(\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)-\left(\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3}{2}+B\,a^3+\frac{3\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)-64\,A^2\,B\,a^9-192\,A^3\,a^8\,b+16\,A^3\,a^3\,b^6+192\,A^3\,a^5\,b^4-32\,A^3\,a^6\,b^3+576\,A^3\,a^7\,b^2+384\,A^2\,B\,a^8\,b-96\,A^2\,C\,a^8\,b+144\,A\,B^2\,a^5\,b^4+192\,A\,B^2\,a^7\,b^2+96\,A^2\,B\,a^4\,b^5+640\,A^2\,B\,a^6\,b^3-96\,A^2\,B\,a^7\,b^2+9\,A\,C^2\,a^3\,b^6+72\,A\,C^2\,a^5\,b^4+144\,A\,C^2\,a^7\,b^2+24\,A^2\,C\,a^3\,b^6+240\,A^2\,C\,a^5\,b^4-24\,A^2\,C\,a^6\,b^3+576\,A^2\,C\,a^7\,b^2+192\,A\,B\,C\,a^8\,b+72\,A\,B\,C\,a^4\,b^5+336\,A\,B\,C\,a^6\,b^3}\right)\,\left(A\,b^3\,1{}\mathrm{i}+B\,a^3\,2{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{4}+A\,a^2\,b\,6{}\mathrm{i}+B\,a\,b^2\,3{}\mathrm{i}+C\,a^2\,b\,3{}\mathrm{i}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{atan}\left(\frac{A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)+A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)}{64\,A\,B^2\,a^9-64\,A^2\,B\,a^9-192\,A^3\,a^8\,b+16\,A^3\,a^3\,b^6+192\,A^3\,a^5\,b^4-32\,A^3\,a^6\,b^3+576\,A^3\,a^7\,b^2+384\,A^2\,B\,a^8\,b-96\,A^2\,C\,a^8\,b+144\,A\,B^2\,a^5\,b^4+192\,A\,B^2\,a^7\,b^2+96\,A^2\,B\,a^4\,b^5+640\,A^2\,B\,a^6\,b^3-96\,A^2\,B\,a^7\,b^2+9\,A\,C^2\,a^3\,b^6+72\,A\,C^2\,a^5\,b^4+144\,A\,C^2\,a^7\,b^2+24\,A^2\,C\,a^3\,b^6+240\,A^2\,C\,a^5\,b^4-24\,A^2\,C\,a^6\,b^3+576\,A^2\,C\,a^7\,b^2+192\,A\,B\,C\,a^8\,b+72\,A\,B\,C\,a^4\,b^5+336\,A\,B\,C\,a^6\,b^3+A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)}{d}","Not used",1,"(atan(((((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) + tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2)*1i - (((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) - tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2)*1i)/(64*A*B^2*a^9 - (((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) - tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2) - (((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) + tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3)/2 + B*a^3 + (3*C*b^3)/8 + 3*A*a^2*b + (3*B*a*b^2)/2 + (3*C*a^2*b)/2) - 64*A^2*B*a^9 - 192*A^3*a^8*b + 16*A^3*a^3*b^6 + 192*A^3*a^5*b^4 - 32*A^3*a^6*b^3 + 576*A^3*a^7*b^2 + 384*A^2*B*a^8*b - 96*A^2*C*a^8*b + 144*A*B^2*a^5*b^4 + 192*A*B^2*a^7*b^2 + 96*A^2*B*a^4*b^5 + 640*A^2*B*a^6*b^3 - 96*A^2*B*a^7*b^2 + 9*A*C^2*a^3*b^6 + 72*A*C^2*a^5*b^4 + 144*A*C^2*a^7*b^2 + 24*A^2*C*a^3*b^6 + 240*A^2*C*a^5*b^4 - 24*A^2*C*a^6*b^3 + 576*A^2*C*a^7*b^2 + 192*A*B*C*a^8*b + 72*A*B*C*a^4*b^5 + 336*A*B*C*a^6*b^3))*(A*b^3*1i + B*a^3*2i + (C*b^3*3i)/4 + A*a^2*b*6i + B*a*b^2*3i + C*a^2*b*3i))/d - (tan(c/2 + (d*x)/2)^7*(2*B*b^3 - A*b^3 + 2*C*a^3 - (5*C*b^3)/4 + 6*A*a*b^2 - 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(A*b^3 + (10*B*b^3)/3 + 6*C*a^3 - (3*C*b^3)/4 + 18*A*a*b^2 + 3*B*a*b^2 + 18*B*a^2*b + 10*C*a*b^2 + 3*C*a^2*b) - tan(c/2 + (d*x)/2)^5*((10*B*b^3)/3 - A*b^3 + 6*C*a^3 + (3*C*b^3)/4 + 18*A*a*b^2 - 3*B*a*b^2 + 18*B*a^2*b + 10*C*a*b^2 - 3*C*a^2*b) - tan(c/2 + (d*x)/2)*(A*b^3 + 2*B*b^3 + 2*C*a^3 + (5*C*b^3)/4 + 6*A*a*b^2 + 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (2*A*a^3*atan((A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) - A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b)*1i) + A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) + A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b)*1i))/(64*A*B^2*a^9 - 64*A^2*B*a^9 - 192*A^3*a^8*b + A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) - A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b)*1i)*1i - A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) + A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b)*1i)*1i + 16*A^3*a^3*b^6 + 192*A^3*a^5*b^4 - 32*A^3*a^6*b^3 + 576*A^3*a^7*b^2 + 384*A^2*B*a^8*b - 96*A^2*C*a^8*b + 144*A*B^2*a^5*b^4 + 192*A*B^2*a^7*b^2 + 96*A^2*B*a^4*b^5 + 640*A^2*B*a^6*b^3 - 96*A^2*B*a^7*b^2 + 9*A*C^2*a^3*b^6 + 72*A*C^2*a^5*b^4 + 144*A*C^2*a^7*b^2 + 24*A^2*C*a^3*b^6 + 240*A^2*C*a^5*b^4 - 24*A^2*C*a^6*b^3 + 576*A^2*C*a^7*b^2 + 192*A*B*C*a^8*b + 72*A*B*C*a^4*b^5 + 336*A*B*C*a^6*b^3)))/d","B"
881,1,2437,192,6.487316,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","-\frac{\left(2\,A\,b^3-2\,A\,a^3-B\,b^3+2\,C\,b^3+6\,B\,a\,b^2-3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a^3-2\,A\,b^3-B\,b^3+\frac{2\,C\,b^3}{3}-6\,B\,a\,b^2-3\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(B\,b^3-2\,A\,b^3-6\,A\,a^3+\frac{2\,C\,b^3}{3}-6\,B\,a\,b^2+3\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+2\,A\,b^3+B\,b^3+2\,C\,b^3+6\,B\,a\,b^2+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b+\frac{3\,C\,a\,b^2}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)}{64\,B\,C^2\,a^9-2\,{\left(\frac{B\,b^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b+\frac{3\,C\,a\,b^2}{2}\right)}^2\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)-64\,B^2\,C\,a^9-192\,B^3\,a^8\,b+1728\,A^3\,a^4\,b^5-1728\,A^3\,a^5\,b^4+16\,B^3\,a^3\,b^6+192\,B^3\,a^5\,b^4-32\,B^3\,a^6\,b^3+576\,B^3\,a^7\,b^2+192\,A\,C^2\,a^8\,b+384\,B^2\,C\,a^8\,b+48\,A\,B^2\,a^2\,b^7+768\,A\,B^2\,a^4\,b^5-192\,A\,B^2\,a^5\,b^4+2880\,A\,B^2\,a^6\,b^3-1344\,A\,B^2\,a^7\,b^2+576\,A^2\,B\,a^3\,b^6-288\,A^2\,B\,a^4\,b^5+4032\,A^2\,B\,a^5\,b^4-2880\,A^2\,B\,a^6\,b^3+432\,A\,C^2\,a^4\,b^5+576\,A\,C^2\,a^6\,b^3+1728\,A^2\,C\,a^4\,b^5-864\,A^2\,C\,a^5\,b^4+1152\,A^2\,C\,a^6\,b^3-576\,A^2\,C\,a^7\,b^2+144\,B\,C^2\,a^5\,b^4+192\,B\,C^2\,a^7\,b^2+96\,B^2\,C\,a^4\,b^5+640\,B^2\,C\,a^6\,b^3-96\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a^8\,b+288\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^5\,b^4-576\,A\,B\,C\,a^6\,b^3+1536\,A\,B\,C\,a^7\,b^2}\right)\,\left(B\,b^3+2\,C\,a^3+6\,A\,a\,b^2+6\,B\,a^2\,b+3\,C\,a\,b^2\right)}{d}+\frac{2\,a^2\,\mathrm{atan}\left(\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)-a^2\,\left(3\,A\,b+B\,a\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)\,\left(3\,A\,b+B\,a\right)+a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)+a^2\,\left(3\,A\,b+B\,a\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)\,\left(3\,A\,b+B\,a\right)}{64\,B\,C^2\,a^9-64\,B^2\,C\,a^9-192\,B^3\,a^8\,b+1728\,A^3\,a^4\,b^5-1728\,A^3\,a^5\,b^4+16\,B^3\,a^3\,b^6+192\,B^3\,a^5\,b^4-32\,B^3\,a^6\,b^3+576\,B^3\,a^7\,b^2+192\,A\,C^2\,a^8\,b+384\,B^2\,C\,a^8\,b+48\,A\,B^2\,a^2\,b^7+768\,A\,B^2\,a^4\,b^5-192\,A\,B^2\,a^5\,b^4+2880\,A\,B^2\,a^6\,b^3-1344\,A\,B^2\,a^7\,b^2+576\,A^2\,B\,a^3\,b^6-288\,A^2\,B\,a^4\,b^5+4032\,A^2\,B\,a^5\,b^4-2880\,A^2\,B\,a^6\,b^3+432\,A\,C^2\,a^4\,b^5+576\,A\,C^2\,a^6\,b^3+1728\,A^2\,C\,a^4\,b^5-864\,A^2\,C\,a^5\,b^4+1152\,A^2\,C\,a^6\,b^3-576\,A^2\,C\,a^7\,b^2+144\,B\,C^2\,a^5\,b^4+192\,B\,C^2\,a^7\,b^2+96\,B^2\,C\,a^4\,b^5+640\,B^2\,C\,a^6\,b^3-96\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a^8\,b+288\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^5\,b^4-576\,A\,B\,C\,a^6\,b^3+1536\,A\,B\,C\,a^7\,b^2+a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)-a^2\,\left(3\,A\,b+B\,a\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)\,\left(3\,A\,b+B\,a\right)\,1{}\mathrm{i}-a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)+a^2\,\left(3\,A\,b+B\,a\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)\,\left(3\,A\,b+B\,a\right)\,1{}\mathrm{i}}\right)\,\left(3\,A\,b+B\,a\right)}{d}","Not used",1,"(2*a^2*atan((a^2*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3) - a^2*(3*A*b + B*a)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2)*1i)*(3*A*b + B*a) + a^2*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3) + a^2*(3*A*b + B*a)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2)*1i)*(3*A*b + B*a))/(64*B*C^2*a^9 - 64*B^2*C*a^9 - 192*B^3*a^8*b + 1728*A^3*a^4*b^5 - 1728*A^3*a^5*b^4 + 16*B^3*a^3*b^6 + 192*B^3*a^5*b^4 - 32*B^3*a^6*b^3 + 576*B^3*a^7*b^2 + a^2*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3) - a^2*(3*A*b + B*a)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2)*1i)*(3*A*b + B*a)*1i - a^2*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3) + a^2*(3*A*b + B*a)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2)*1i)*(3*A*b + B*a)*1i + 192*A*C^2*a^8*b + 384*B^2*C*a^8*b + 48*A*B^2*a^2*b^7 + 768*A*B^2*a^4*b^5 - 192*A*B^2*a^5*b^4 + 2880*A*B^2*a^6*b^3 - 1344*A*B^2*a^7*b^2 + 576*A^2*B*a^3*b^6 - 288*A^2*B*a^4*b^5 + 4032*A^2*B*a^5*b^4 - 2880*A^2*B*a^6*b^3 + 432*A*C^2*a^4*b^5 + 576*A*C^2*a^6*b^3 + 1728*A^2*C*a^4*b^5 - 864*A^2*C*a^5*b^4 + 1152*A^2*C*a^6*b^3 - 576*A^2*C*a^7*b^2 + 144*B*C^2*a^5*b^4 + 192*B*C^2*a^7*b^2 + 96*B^2*C*a^4*b^5 + 640*B^2*C*a^6*b^3 - 96*B^2*C*a^7*b^2 - 384*A*B*C*a^8*b + 288*A*B*C*a^3*b^6 + 2496*A*B*C*a^5*b^4 - 576*A*B*C*a^6*b^3 + 1536*A*B*C*a^7*b^2))*(3*A*b + B*a))/d - (atanh((2*tan(c/2 + (d*x)/2)*((B*b^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b + (3*C*a*b^2)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3))/(64*B*C^2*a^9 - 2*((B*b^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b + (3*C*a*b^2)/2)^2*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2) - 64*B^2*C*a^9 - 192*B^3*a^8*b + 1728*A^3*a^4*b^5 - 1728*A^3*a^5*b^4 + 16*B^3*a^3*b^6 + 192*B^3*a^5*b^4 - 32*B^3*a^6*b^3 + 576*B^3*a^7*b^2 + 192*A*C^2*a^8*b + 384*B^2*C*a^8*b + 48*A*B^2*a^2*b^7 + 768*A*B^2*a^4*b^5 - 192*A*B^2*a^5*b^4 + 2880*A*B^2*a^6*b^3 - 1344*A*B^2*a^7*b^2 + 576*A^2*B*a^3*b^6 - 288*A^2*B*a^4*b^5 + 4032*A^2*B*a^5*b^4 - 2880*A^2*B*a^6*b^3 + 432*A*C^2*a^4*b^5 + 576*A*C^2*a^6*b^3 + 1728*A^2*C*a^4*b^5 - 864*A^2*C*a^5*b^4 + 1152*A^2*C*a^6*b^3 - 576*A^2*C*a^7*b^2 + 144*B*C^2*a^5*b^4 + 192*B*C^2*a^7*b^2 + 96*B^2*C*a^4*b^5 + 640*B^2*C*a^6*b^3 - 96*B^2*C*a^7*b^2 - 384*A*B*C*a^8*b + 288*A*B*C*a^3*b^6 + 2496*A*B*C*a^5*b^4 - 576*A*B*C*a^6*b^3 + 1536*A*B*C*a^7*b^2))*(B*b^3 + 2*C*a^3 + 6*A*a*b^2 + 6*B*a^2*b + 3*C*a*b^2))/d - (tan(c/2 + (d*x)/2)*(2*A*a^3 + 2*A*b^3 + B*b^3 + 2*C*b^3 + 6*B*a*b^2 + 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^7*(2*A*b^3 - 2*A*a^3 - B*b^3 + 2*C*b^3 + 6*B*a*b^2 - 3*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*(6*A*a^3 + 2*A*b^3 - B*b^3 - (2*C*b^3)/3 + 6*B*a*b^2 - 3*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^5*(2*A*b^3 - 6*A*a^3 + B*b^3 - (2*C*b^3)/3 + 6*B*a*b^2 + 3*C*a*b^2 + 6*C*a^2*b))/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 - 1))","B"
882,1,3879,204,7.199179,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","-\frac{\mathrm{atan}\left(\frac{\left(\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,1{}\mathrm{i}-\left(\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,1{}\mathrm{i}}{\left(\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)+\left(\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(A\,b^3+\frac{C\,b^3}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)-192\,A^3\,a\,b^8+192\,C^3\,a^8\,b+576\,A^3\,a^2\,b^7-32\,A^3\,a^3\,b^6+192\,A^3\,a^4\,b^5+16\,A^3\,a^6\,b^3-1728\,B^3\,a^4\,b^5+1728\,B^3\,a^5\,b^4-16\,C^3\,a^3\,b^6-192\,C^3\,a^5\,b^4+32\,C^3\,a^6\,b^3-576\,C^3\,a^7\,b^2-48\,A\,C^2\,a\,b^8+192\,A\,C^2\,a^8\,b-192\,A^2\,C\,a\,b^8+48\,A^2\,C\,a^8\,b-2880\,A\,B^2\,a^3\,b^6+4032\,A\,B^2\,a^4\,b^5-288\,A\,B^2\,a^5\,b^4+576\,A\,B^2\,a^6\,b^3-1344\,A^2\,B\,a^2\,b^7+2880\,A^2\,B\,a^3\,b^6-192\,A^2\,B\,a^4\,b^5+768\,A^2\,B\,a^5\,b^4+48\,A^2\,B\,a^7\,b^2-648\,A\,C^2\,a^3\,b^6+192\,A\,C^2\,a^4\,b^5-2208\,A\,C^2\,a^5\,b^4+1248\,A\,C^2\,a^6\,b^3-288\,A\,C^2\,a^7\,b^2+288\,A^2\,C\,a^2\,b^7-1248\,A^2\,C\,a^3\,b^6+2208\,A^2\,C\,a^4\,b^5-192\,A^2\,C\,a^5\,b^4+648\,A^2\,C\,a^6\,b^3-48\,B\,C^2\,a^2\,b^7-768\,B\,C^2\,a^4\,b^5+192\,B\,C^2\,a^5\,b^4-2880\,B\,C^2\,a^6\,b^3+1344\,B\,C^2\,a^7\,b^2-576\,B^2\,C\,a^3\,b^6+288\,B^2\,C\,a^4\,b^5-4032\,B^2\,C\,a^5\,b^4+2880\,B^2\,C\,a^6\,b^3-768\,A\,B\,C\,a^2\,b^7+576\,A\,B\,C\,a^3\,b^6-5088\,A\,B\,C\,a^4\,b^5+5088\,A\,B\,C\,a^5\,b^4-576\,A\,B\,C\,a^6\,b^3+768\,A\,B\,C\,a^7\,b^2}\right)\,\left(A\,b^3\,2{}\mathrm{i}+C\,b^3\,1{}\mathrm{i}+B\,a\,b^2\,6{}\mathrm{i}+C\,a^2\,b\,6{}\mathrm{i}\right)}{d}-\frac{\left(A\,a^3-2\,B\,a^3+2\,B\,b^3-C\,b^3-6\,A\,a^2\,b+6\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(2\,B\,a^3-3\,A\,a^3+2\,B\,b^3-3\,C\,b^3+6\,A\,a^2\,b+6\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(3\,A\,a^3+2\,B\,a^3-2\,B\,b^3-3\,C\,b^3+6\,A\,a^2\,b-6\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-A\,a^3-2\,B\,a^3-2\,B\,b^3-C\,b^3-6\,A\,a^2\,b-6\,C\,a\,b^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)-\frac{a\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)}{2}+\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)+\frac{a\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)}{2}}{192\,A^3\,a\,b^8-192\,C^3\,a^8\,b-576\,A^3\,a^2\,b^7+32\,A^3\,a^3\,b^6-192\,A^3\,a^4\,b^5-16\,A^3\,a^6\,b^3+1728\,B^3\,a^4\,b^5-1728\,B^3\,a^5\,b^4+16\,C^3\,a^3\,b^6+192\,C^3\,a^5\,b^4-32\,C^3\,a^6\,b^3+576\,C^3\,a^7\,b^2+48\,A\,C^2\,a\,b^8-192\,A\,C^2\,a^8\,b+192\,A^2\,C\,a\,b^8-48\,A^2\,C\,a^8\,b+2880\,A\,B^2\,a^3\,b^6-4032\,A\,B^2\,a^4\,b^5+288\,A\,B^2\,a^5\,b^4-576\,A\,B^2\,a^6\,b^3+1344\,A^2\,B\,a^2\,b^7-2880\,A^2\,B\,a^3\,b^6+192\,A^2\,B\,a^4\,b^5-768\,A^2\,B\,a^5\,b^4-48\,A^2\,B\,a^7\,b^2+648\,A\,C^2\,a^3\,b^6-192\,A\,C^2\,a^4\,b^5+2208\,A\,C^2\,a^5\,b^4-1248\,A\,C^2\,a^6\,b^3+288\,A\,C^2\,a^7\,b^2-288\,A^2\,C\,a^2\,b^7+1248\,A^2\,C\,a^3\,b^6-2208\,A^2\,C\,a^4\,b^5+192\,A^2\,C\,a^5\,b^4-648\,A^2\,C\,a^6\,b^3+48\,B\,C^2\,a^2\,b^7+768\,B\,C^2\,a^4\,b^5-192\,B\,C^2\,a^5\,b^4+2880\,B\,C^2\,a^6\,b^3-1344\,B\,C^2\,a^7\,b^2+576\,B^2\,C\,a^3\,b^6-288\,B^2\,C\,a^4\,b^5+4032\,B^2\,C\,a^5\,b^4-2880\,B^2\,C\,a^6\,b^3+768\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+5088\,A\,B\,C\,a^4\,b^5-5088\,A\,B\,C\,a^5\,b^4+576\,A\,B\,C\,a^6\,b^3-768\,A\,B\,C\,a^7\,b^2+\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)-\frac{a\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)\,1{}\mathrm{i}}{2}-\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)+\frac{a\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)\,1{}\mathrm{i}}{2}}\right)\,\left(A\,a^2+6\,A\,b^2+2\,C\,a^2+6\,B\,a\,b\right)}{d}","Not used",1,"(a*atan(((a*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) - (a*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b))/2 + (a*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) + (a*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b))/2)/(192*A^3*a*b^8 - 192*C^3*a^8*b + (a*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) - (a*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b)*1i)/2 - (a*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) + (a*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b)*1i)/2 - 576*A^3*a^2*b^7 + 32*A^3*a^3*b^6 - 192*A^3*a^4*b^5 - 16*A^3*a^6*b^3 + 1728*B^3*a^4*b^5 - 1728*B^3*a^5*b^4 + 16*C^3*a^3*b^6 + 192*C^3*a^5*b^4 - 32*C^3*a^6*b^3 + 576*C^3*a^7*b^2 + 48*A*C^2*a*b^8 - 192*A*C^2*a^8*b + 192*A^2*C*a*b^8 - 48*A^2*C*a^8*b + 2880*A*B^2*a^3*b^6 - 4032*A*B^2*a^4*b^5 + 288*A*B^2*a^5*b^4 - 576*A*B^2*a^6*b^3 + 1344*A^2*B*a^2*b^7 - 2880*A^2*B*a^3*b^6 + 192*A^2*B*a^4*b^5 - 768*A^2*B*a^5*b^4 - 48*A^2*B*a^7*b^2 + 648*A*C^2*a^3*b^6 - 192*A*C^2*a^4*b^5 + 2208*A*C^2*a^5*b^4 - 1248*A*C^2*a^6*b^3 + 288*A*C^2*a^7*b^2 - 288*A^2*C*a^2*b^7 + 1248*A^2*C*a^3*b^6 - 2208*A^2*C*a^4*b^5 + 192*A^2*C*a^5*b^4 - 648*A^2*C*a^6*b^3 + 48*B*C^2*a^2*b^7 + 768*B*C^2*a^4*b^5 - 192*B*C^2*a^5*b^4 + 2880*B*C^2*a^6*b^3 - 1344*B*C^2*a^7*b^2 + 576*B^2*C*a^3*b^6 - 288*B^2*C*a^4*b^5 + 4032*B^2*C*a^5*b^4 - 2880*B^2*C*a^6*b^3 + 768*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 5088*A*B*C*a^4*b^5 - 5088*A*B*C*a^5*b^4 + 576*A*B*C*a^6*b^3 - 768*A*B*C*a^7*b^2))*(A*a^2 + 6*A*b^2 + 2*C*a^2 + 6*B*a*b))/d - (tan(c/2 + (d*x)/2)^7*(A*a^3 - 2*B*a^3 + 2*B*b^3 - C*b^3 - 6*A*a^2*b + 6*C*a*b^2) + tan(c/2 + (d*x)/2)^3*(3*A*a^3 + 2*B*a^3 - 2*B*b^3 - 3*C*b^3 + 6*A*a^2*b - 6*C*a*b^2) + tan(c/2 + (d*x)/2)^5*(2*B*a^3 - 3*A*a^3 + 2*B*b^3 - 3*C*b^3 + 6*A*a^2*b + 6*C*a*b^2) - tan(c/2 + (d*x)/2)*(A*a^3 + 2*B*a^3 + 2*B*b^3 + C*b^3 + 6*A*a^2*b + 6*C*a*b^2))/(d*(tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^4 + 1)) - (atan((((A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b)*1i - ((A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b)*1i)/(((A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b) + ((A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(A*b^3 + (C*b^3)/2 + 3*B*a*b^2 + 3*C*a^2*b) - 192*A^3*a*b^8 + 192*C^3*a^8*b + 576*A^3*a^2*b^7 - 32*A^3*a^3*b^6 + 192*A^3*a^4*b^5 + 16*A^3*a^6*b^3 - 1728*B^3*a^4*b^5 + 1728*B^3*a^5*b^4 - 16*C^3*a^3*b^6 - 192*C^3*a^5*b^4 + 32*C^3*a^6*b^3 - 576*C^3*a^7*b^2 - 48*A*C^2*a*b^8 + 192*A*C^2*a^8*b - 192*A^2*C*a*b^8 + 48*A^2*C*a^8*b - 2880*A*B^2*a^3*b^6 + 4032*A*B^2*a^4*b^5 - 288*A*B^2*a^5*b^4 + 576*A*B^2*a^6*b^3 - 1344*A^2*B*a^2*b^7 + 2880*A^2*B*a^3*b^6 - 192*A^2*B*a^4*b^5 + 768*A^2*B*a^5*b^4 + 48*A^2*B*a^7*b^2 - 648*A*C^2*a^3*b^6 + 192*A*C^2*a^4*b^5 - 2208*A*C^2*a^5*b^4 + 1248*A*C^2*a^6*b^3 - 288*A*C^2*a^7*b^2 + 288*A^2*C*a^2*b^7 - 1248*A^2*C*a^3*b^6 + 2208*A^2*C*a^4*b^5 - 192*A^2*C*a^5*b^4 + 648*A^2*C*a^6*b^3 - 48*B*C^2*a^2*b^7 - 768*B*C^2*a^4*b^5 + 192*B*C^2*a^5*b^4 - 2880*B*C^2*a^6*b^3 + 1344*B*C^2*a^7*b^2 - 576*B^2*C*a^3*b^6 + 288*B^2*C*a^4*b^5 - 4032*B^2*C*a^5*b^4 + 2880*B^2*C*a^6*b^3 - 768*A*B*C*a^2*b^7 + 576*A*B*C*a^3*b^6 - 5088*A*B*C*a^4*b^5 + 5088*A*B*C*a^5*b^4 - 576*A*B*C*a^6*b^3 + 768*A*B*C*a^7*b^2))*(A*b^3*2i + C*b^3*1i + B*a*b^2*6i + C*a^2*b*6i))/d","B"
883,1,2470,196,6.410395,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(B\,a^3-2\,A\,a^3-2\,C\,a^3+2\,C\,b^3-6\,A\,a\,b^2+3\,A\,a^2\,b-6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{2\,A\,a^3}{3}-B\,a^3-2\,C\,a^3+6\,C\,b^3-6\,A\,a\,b^2-3\,A\,a^2\,b-6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,C\,a^3-B\,a^3-\frac{2\,A\,a^3}{3}+6\,C\,b^3+6\,A\,a\,b^2-3\,A\,a^2\,b+6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+B\,a^3+2\,C\,a^3+2\,C\,b^3+6\,A\,a\,b^2+3\,A\,a^2\,b+6\,B\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(B\,b^3+3\,C\,a\,b^2\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)\right)\,\left(B\,b^3+3\,C\,a\,b^2\right)\,1{}\mathrm{i}-\left(\left(B\,b^3+3\,C\,a\,b^2\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)\right)\,\left(B\,b^3+3\,C\,a\,b^2\right)\,1{}\mathrm{i}}{\left(\left(B\,b^3+3\,C\,a\,b^2\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)\right)\,\left(B\,b^3+3\,C\,a\,b^2\right)+\left(\left(B\,b^3+3\,C\,a\,b^2\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)\right)\,\left(B\,b^3+3\,C\,a\,b^2\right)-64\,A\,B^2\,b^9+64\,A^2\,B\,b^9-192\,B^3\,a\,b^8+576\,B^3\,a^2\,b^7-32\,B^3\,a^3\,b^6+192\,B^3\,a^4\,b^5+16\,B^3\,a^6\,b^3-1728\,C^3\,a^4\,b^5+1728\,C^3\,a^5\,b^4+384\,A\,B^2\,a\,b^8+192\,A^2\,C\,a\,b^8-96\,A\,B^2\,a^2\,b^7+640\,A\,B^2\,a^3\,b^6+96\,A\,B^2\,a^5\,b^4+192\,A^2\,B\,a^2\,b^7+144\,A^2\,B\,a^4\,b^5-576\,A\,C^2\,a^2\,b^7+1152\,A\,C^2\,a^3\,b^6-864\,A\,C^2\,a^4\,b^5+1728\,A\,C^2\,a^5\,b^4+576\,A^2\,C\,a^3\,b^6+432\,A^2\,C\,a^5\,b^4-2880\,B\,C^2\,a^3\,b^6+4032\,B\,C^2\,a^4\,b^5-288\,B\,C^2\,a^5\,b^4+576\,B\,C^2\,a^6\,b^3-1344\,B^2\,C\,a^2\,b^7+2880\,B^2\,C\,a^3\,b^6-192\,B^2\,C\,a^4\,b^5+768\,B^2\,C\,a^5\,b^4+48\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a\,b^8+1536\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^4\,b^5+288\,A\,B\,C\,a^6\,b^3}\right)\,\left(2{}\mathrm{i}\,B\,b^3+6{}\mathrm{i}\,C\,a\,b^2\right)}{d}+\frac{\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,1{}\mathrm{i}+\frac{B\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a^2\,b\,3{}\mathrm{i}}{2}+B\,a\,b^2\,3{}\mathrm{i}+C\,a^2\,b\,3{}\mathrm{i}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)}{2\,{\left(A\,b^3\,1{}\mathrm{i}+\frac{B\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a^2\,b\,3{}\mathrm{i}}{2}+B\,a\,b^2\,3{}\mathrm{i}+C\,a^2\,b\,3{}\mathrm{i}\right)}^2\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)-64\,A\,B^2\,b^9+64\,A^2\,B\,b^9-192\,B^3\,a\,b^8+576\,B^3\,a^2\,b^7-32\,B^3\,a^3\,b^6+192\,B^3\,a^4\,b^5+16\,B^3\,a^6\,b^3-1728\,C^3\,a^4\,b^5+1728\,C^3\,a^5\,b^4+384\,A\,B^2\,a\,b^8+192\,A^2\,C\,a\,b^8-96\,A\,B^2\,a^2\,b^7+640\,A\,B^2\,a^3\,b^6+96\,A\,B^2\,a^5\,b^4+192\,A^2\,B\,a^2\,b^7+144\,A^2\,B\,a^4\,b^5-576\,A\,C^2\,a^2\,b^7+1152\,A\,C^2\,a^3\,b^6-864\,A\,C^2\,a^4\,b^5+1728\,A\,C^2\,a^5\,b^4+576\,A^2\,C\,a^3\,b^6+432\,A^2\,C\,a^5\,b^4-2880\,B\,C^2\,a^3\,b^6+4032\,B\,C^2\,a^4\,b^5-288\,B\,C^2\,a^5\,b^4+576\,B\,C^2\,a^6\,b^3-1344\,B^2\,C\,a^2\,b^7+2880\,B^2\,C\,a^3\,b^6-192\,B^2\,C\,a^4\,b^5+768\,B^2\,C\,a^5\,b^4+48\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a\,b^8+1536\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^4\,b^5+288\,A\,B\,C\,a^6\,b^3}\right)\,\left(A\,b^3\,2{}\mathrm{i}+B\,a^3\,1{}\mathrm{i}+A\,a^2\,b\,3{}\mathrm{i}+B\,a\,b^2\,6{}\mathrm{i}+C\,a^2\,b\,6{}\mathrm{i}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^3 + B*a^3 + 2*C*a^3 + 2*C*b^3 + 6*A*a*b^2 + 3*A*a^2*b + 6*B*a^2*b) - tan(c/2 + (d*x)/2)^7*(2*A*a^3 - B*a^3 + 2*C*a^3 - 2*C*b^3 + 6*A*a*b^2 - 3*A*a^2*b + 6*B*a^2*b) + tan(c/2 + (d*x)/2)^3*(2*C*a^3 - B*a^3 - (2*A*a^3)/3 + 6*C*b^3 + 6*A*a*b^2 - 3*A*a^2*b + 6*B*a^2*b) - tan(c/2 + (d*x)/2)^5*(B*a^3 - (2*A*a^3)/3 + 2*C*a^3 - 6*C*b^3 + 6*A*a*b^2 + 3*A*a^2*b + 6*B*a^2*b))/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + 1)) - (atan((((B*b^3 + 3*C*a*b^2)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(B*b^3 + 3*C*a*b^2)*1i - ((B*b^3 + 3*C*a*b^2)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(B*b^3 + 3*C*a*b^2)*1i)/(((B*b^3 + 3*C*a*b^2)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(B*b^3 + 3*C*a*b^2) + ((B*b^3 + 3*C*a*b^2)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*(B*b^3 + 3*C*a*b^2) - 64*A*B^2*b^9 + 64*A^2*B*b^9 - 192*B^3*a*b^8 + 576*B^3*a^2*b^7 - 32*B^3*a^3*b^6 + 192*B^3*a^4*b^5 + 16*B^3*a^6*b^3 - 1728*C^3*a^4*b^5 + 1728*C^3*a^5*b^4 + 384*A*B^2*a*b^8 + 192*A^2*C*a*b^8 - 96*A*B^2*a^2*b^7 + 640*A*B^2*a^3*b^6 + 96*A*B^2*a^5*b^4 + 192*A^2*B*a^2*b^7 + 144*A^2*B*a^4*b^5 - 576*A*C^2*a^2*b^7 + 1152*A*C^2*a^3*b^6 - 864*A*C^2*a^4*b^5 + 1728*A*C^2*a^5*b^4 + 576*A^2*C*a^3*b^6 + 432*A^2*C*a^5*b^4 - 2880*B*C^2*a^3*b^6 + 4032*B*C^2*a^4*b^5 - 288*B*C^2*a^5*b^4 + 576*B*C^2*a^6*b^3 - 1344*B^2*C*a^2*b^7 + 2880*B^2*C*a^3*b^6 - 192*B^2*C*a^4*b^5 + 768*B^2*C*a^5*b^4 + 48*B^2*C*a^7*b^2 - 384*A*B*C*a*b^8 + 1536*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 2496*A*B*C*a^4*b^5 + 288*A*B*C*a^6*b^3))*(B*b^3*2i + C*a*b^2*6i))/d + (atanh((2*tan(c/2 + (d*x)/2)*(A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i + C*a^2*b*3i)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3))/(2*(A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i + C*a^2*b*3i)^2*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b) - 64*A*B^2*b^9 + 64*A^2*B*b^9 - 192*B^3*a*b^8 + 576*B^3*a^2*b^7 - 32*B^3*a^3*b^6 + 192*B^3*a^4*b^5 + 16*B^3*a^6*b^3 - 1728*C^3*a^4*b^5 + 1728*C^3*a^5*b^4 + 384*A*B^2*a*b^8 + 192*A^2*C*a*b^8 - 96*A*B^2*a^2*b^7 + 640*A*B^2*a^3*b^6 + 96*A*B^2*a^5*b^4 + 192*A^2*B*a^2*b^7 + 144*A^2*B*a^4*b^5 - 576*A*C^2*a^2*b^7 + 1152*A*C^2*a^3*b^6 - 864*A*C^2*a^4*b^5 + 1728*A*C^2*a^5*b^4 + 576*A^2*C*a^3*b^6 + 432*A^2*C*a^5*b^4 - 2880*B*C^2*a^3*b^6 + 4032*B*C^2*a^4*b^5 - 288*B*C^2*a^5*b^4 + 576*B*C^2*a^6*b^3 - 1344*B^2*C*a^2*b^7 + 2880*B^2*C*a^3*b^6 - 192*B^2*C*a^4*b^5 + 768*B^2*C*a^5*b^4 + 48*B^2*C*a^7*b^2 - 384*A*B*C*a*b^8 + 1536*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 2496*A*B*C*a^4*b^5 + 288*A*B*C*a^6*b^3))*(A*b^3*2i + B*a^3*1i + A*a^2*b*3i + B*a*b^2*6i + C*a^2*b*6i))/d","B"
884,1,3250,223,7.313876,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)+\left(\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3\,3{}\mathrm{i}}{8}+B\,b^3\,1{}\mathrm{i}+\frac{C\,a^3\,1{}\mathrm{i}}{2}+\frac{A\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{B\,a^2\,b\,3{}\mathrm{i}}{2}+C\,a\,b^2\,3{}\mathrm{i}\right)-64\,B\,C^2\,b^9+64\,B^2\,C\,b^9-192\,C^3\,a\,b^8+576\,C^3\,a^2\,b^7-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3-96\,A\,C^2\,a\,b^8+384\,B\,C^2\,a\,b^8+576\,A\,C^2\,a^2\,b^7-24\,A\,C^2\,a^3\,b^6+240\,A\,C^2\,a^4\,b^5+24\,A\,C^2\,a^6\,b^3+144\,A^2\,C\,a^2\,b^7+72\,A^2\,C\,a^4\,b^5+9\,A^2\,C\,a^6\,b^3-96\,B\,C^2\,a^2\,b^7+640\,B\,C^2\,a^3\,b^6+96\,B\,C^2\,a^5\,b^4+192\,B^2\,C\,a^2\,b^7+144\,B^2\,C\,a^4\,b^5+192\,A\,B\,C\,a\,b^8+336\,A\,B\,C\,a^3\,b^6+72\,A\,B\,C\,a^5\,b^4}\right)\,\left(\frac{3\,A\,a^3}{4}+2\,B\,b^3+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b+6\,C\,a\,b^2\right)}{d}+\frac{\left(2\,A\,b^3-\frac{5\,A\,a^3}{4}+2\,B\,a^3-C\,a^3-3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,a^2\,b+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a^3}{4}+6\,A\,b^3+\frac{10\,B\,a^3}{3}-C\,a^3-3\,A\,a\,b^2+10\,A\,a^2\,b+18\,B\,a\,b^2-3\,B\,a^2\,b+18\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,b^3-\frac{3\,A\,a^3}{4}+\frac{10\,B\,a^3}{3}+C\,a^3+3\,A\,a\,b^2+10\,A\,a^2\,b+18\,B\,a\,b^2+3\,B\,a^2\,b+18\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a^3}{4}+2\,A\,b^3+2\,B\,a^3+C\,a^3+3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2+3\,B\,a^2\,b+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{C\,b^3\,\mathrm{atan}\left(\frac{C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}}{64\,B^2\,C\,b^9-64\,B\,C^2\,b^9-192\,C^3\,a\,b^8+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)-C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\right)+576\,C^3\,a^2\,b^7-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3-96\,A\,C^2\,a\,b^8+384\,B\,C^2\,a\,b^8+576\,A\,C^2\,a^2\,b^7-24\,A\,C^2\,a^3\,b^6+240\,A\,C^2\,a^4\,b^5+24\,A\,C^2\,a^6\,b^3+144\,A^2\,C\,a^2\,b^7+72\,A^2\,C\,a^4\,b^5+9\,A^2\,C\,a^6\,b^3-96\,B\,C^2\,a^2\,b^7+640\,B\,C^2\,a^3\,b^6+96\,B\,C^2\,a^5\,b^4+192\,B^2\,C\,a^2\,b^7+144\,B^2\,C\,a^4\,b^5+192\,A\,B\,C\,a\,b^8+336\,A\,B\,C\,a^3\,b^6+72\,A\,B\,C\,a^5\,b^4}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) + tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*1i - (((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) - tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*1i)/((((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) + tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i) + (((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) - tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((A*a^3*3i)/8 + B*b^3*1i + (C*a^3*1i)/2 + (A*a*b^2*3i)/2 + (B*a^2*b*3i)/2 + C*a*b^2*3i) - 64*B*C^2*b^9 + 64*B^2*C*b^9 - 192*C^3*a*b^8 + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 - 96*A*C^2*a*b^8 + 384*B*C^2*a*b^8 + 576*A*C^2*a^2*b^7 - 24*A*C^2*a^3*b^6 + 240*A*C^2*a^4*b^5 + 24*A*C^2*a^6*b^3 + 144*A^2*C*a^2*b^7 + 72*A^2*C*a^4*b^5 + 9*A^2*C*a^6*b^3 - 96*B*C^2*a^2*b^7 + 640*B*C^2*a^3*b^6 + 96*B*C^2*a^5*b^4 + 192*B^2*C*a^2*b^7 + 144*B^2*C*a^4*b^5 + 192*A*B*C*a*b^8 + 336*A*B*C*a^3*b^6 + 72*A*B*C*a^5*b^4))*((3*A*a^3)/4 + 2*B*b^3 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b + 6*C*a*b^2))/d + (tan(c/2 + (d*x)/2)^7*(2*A*b^3 - (5*A*a^3)/4 + 2*B*a^3 - C*a^3 - 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 - 3*B*a^2*b + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(6*A*b^3 - (3*A*a^3)/4 + (10*B*a^3)/3 + C*a^3 + 3*A*a*b^2 + 10*A*a^2*b + 18*B*a*b^2 + 3*B*a^2*b + 18*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((3*A*a^3)/4 + 6*A*b^3 + (10*B*a^3)/3 - C*a^3 - 3*A*a*b^2 + 10*A*a^2*b + 18*B*a*b^2 - 3*B*a^2*b + 18*C*a^2*b) + tan(c/2 + (d*x)/2)*((5*A*a^3)/4 + 2*A*b^3 + 2*B*a^3 + C*a^3 + 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 + 3*B*a^2*b + 6*C*a^2*b))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (C*b^3*atan((C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) + C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2))*1i + C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) - C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2))*1i)/(64*B^2*C*b^9 - 64*B*C^2*b^9 - 192*C^3*a*b^8 + C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) + C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2)) - C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) - C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2)) + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 - 96*A*C^2*a*b^8 + 384*B*C^2*a*b^8 + 576*A*C^2*a^2*b^7 - 24*A*C^2*a^3*b^6 + 240*A*C^2*a^4*b^5 + 24*A*C^2*a^6*b^3 + 144*A^2*C*a^2*b^7 + 72*A^2*C*a^4*b^5 + 9*A^2*C*a^6*b^3 - 96*B*C^2*a^2*b^7 + 640*B*C^2*a^3*b^6 + 96*B*C^2*a^5*b^4 + 192*B^2*C*a^2*b^7 + 144*B^2*C*a^4*b^5 + 192*A*B*C*a*b^8 + 336*A*B*C*a^3*b^6 + 72*A*B*C*a^5*b^4))*2i)/d","B"
885,1,359,269,4.933089,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{A\,b^3\,x}{2}+\frac{3\,B\,a^3\,x}{8}+C\,b^3\,x+\frac{9\,A\,a^2\,b\,x}{8}+\frac{3\,B\,a\,b^2\,x}{2}+\frac{3\,C\,a^2\,b\,x}{2}+\frac{5\,A\,a^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{B\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{A\,a^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,A\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,A\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,C\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{9\,A\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{9\,B\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(A*b^3*x)/2 + (3*B*a^3*x)/8 + C*b^3*x + (9*A*a^2*b*x)/8 + (3*B*a*b^2*x)/2 + (3*C*a^2*b*x)/2 + (5*A*a^3*sin(c + d*x))/(8*d) + (B*b^3*sin(c + d*x))/d + (3*C*a^3*sin(c + d*x))/(4*d) + (5*A*a^3*sin(3*c + 3*d*x))/(48*d) + (A*a^3*sin(5*c + 5*d*x))/(80*d) + (A*b^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(4*c + 4*d*x))/(32*d) + (C*a^3*sin(3*c + 3*d*x))/(12*d) + (3*A*a^2*b*sin(2*c + 2*d*x))/(4*d) + (A*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*A*a^2*b*sin(4*c + 4*d*x))/(32*d) + (3*B*a*b^2*sin(2*c + 2*d*x))/(4*d) + (B*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*C*a^2*b*sin(2*c + 2*d*x))/(4*d) + (9*A*a*b^2*sin(c + d*x))/(4*d) + (9*B*a^2*b*sin(c + d*x))/(4*d) + (3*C*a*b^2*sin(c + d*x))/d","B"
886,1,471,320,5.819662,"\text{Not used}","int(cos(c + d*x)^6*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{5\,A\,a^3\,x}{16}+\frac{B\,b^3\,x}{2}+\frac{3\,C\,a^3\,x}{8}+\frac{9\,A\,a\,b^2\,x}{8}+\frac{9\,B\,a^2\,b\,x}{8}+\frac{3\,C\,a\,b^2\,x}{2}+\frac{3\,A\,b^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,B\,a^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{15\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{A\,a^3\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{A\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{5\,B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,a^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,A\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,A\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{16\,d}+\frac{3\,A\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,A\,a^2\,b\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{15\,A\,a^2\,b\,\sin\left(c+d\,x\right)}{8\,d}+\frac{9\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{9\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(5*A*a^3*x)/16 + (B*b^3*x)/2 + (3*C*a^3*x)/8 + (9*A*a*b^2*x)/8 + (9*B*a^2*b*x)/8 + (3*C*a*b^2*x)/2 + (3*A*b^3*sin(c + d*x))/(4*d) + (5*B*a^3*sin(c + d*x))/(8*d) + (C*b^3*sin(c + d*x))/d + (15*A*a^3*sin(2*c + 2*d*x))/(64*d) + (3*A*a^3*sin(4*c + 4*d*x))/(64*d) + (A*a^3*sin(6*c + 6*d*x))/(192*d) + (A*b^3*sin(3*c + 3*d*x))/(12*d) + (5*B*a^3*sin(3*c + 3*d*x))/(48*d) + (B*a^3*sin(5*c + 5*d*x))/(80*d) + (B*b^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(4*c + 4*d*x))/(32*d) + (3*A*a*b^2*sin(2*c + 2*d*x))/(4*d) + (5*A*a^2*b*sin(3*c + 3*d*x))/(16*d) + (3*A*a*b^2*sin(4*c + 4*d*x))/(32*d) + (3*A*a^2*b*sin(5*c + 5*d*x))/(80*d) + (3*B*a^2*b*sin(2*c + 2*d*x))/(4*d) + (B*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*B*a^2*b*sin(4*c + 4*d*x))/(32*d) + (3*C*a*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*b*sin(3*c + 3*d*x))/(4*d) + (15*A*a^2*b*sin(c + d*x))/(8*d) + (9*B*a*b^2*sin(c + d*x))/(4*d) + (9*C*a^2*b*sin(c + d*x))/(4*d)","B"
887,1,1044,491,7.748709,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,a^4}{2}+\frac{5\,B\,b^4}{16}+\frac{9\,B\,a^2\,b^2}{4}+\frac{3\,A\,a\,b^3}{2}+2\,A\,a^3\,b+\frac{5\,C\,a\,b^3}{4}+\frac{3\,C\,a^3\,b}{2}\right)}{2\,B\,a^4+\frac{5\,B\,b^4}{4}+9\,B\,a^2\,b^2+6\,A\,a\,b^3+8\,A\,a^3\,b+5\,C\,a\,b^3+6\,C\,a^3\,b}\right)\,\left(B\,a^4+\frac{5\,B\,b^4}{8}+\frac{9\,B\,a^2\,b^2}{2}+3\,A\,a\,b^3+4\,A\,a^3\,b+\frac{5\,C\,a\,b^3}{2}+3\,C\,a^3\,b\right)}{d}-\frac{\left(2\,A\,a^4+2\,A\,b^4-B\,a^4-\frac{11\,B\,b^4}{8}+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2-\frac{15\,B\,a^2\,b^2}{2}+12\,C\,a^2\,b^2-5\,A\,a\,b^3-4\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,a^3\,b-\frac{11\,C\,a\,b^3}{2}-5\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(4\,B\,a^4-\frac{20\,A\,b^4}{3}-12\,A\,a^4+\frac{7\,B\,b^4}{6}-\frac{28\,C\,a^4}{3}-4\,C\,b^4-56\,A\,a^2\,b^2+18\,B\,a^2\,b^2-40\,C\,a^2\,b^2+12\,A\,a\,b^3+16\,A\,a^3\,b-\frac{80\,B\,a\,b^3}{3}-\frac{112\,B\,a^3\,b}{3}+\frac{14\,C\,a\,b^3}{3}+12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(30\,A\,a^4+\frac{226\,A\,b^4}{15}-5\,B\,a^4-\frac{85\,B\,b^4}{24}+\frac{58\,C\,a^4}{3}+\frac{86\,C\,b^4}{5}+116\,A\,a^2\,b^2-\frac{27\,B\,a^2\,b^2}{2}+\frac{452\,C\,a^2\,b^2}{5}-9\,A\,a\,b^3-20\,A\,a^3\,b+\frac{904\,B\,a\,b^3}{15}+\frac{232\,B\,a^3\,b}{3}-\frac{85\,C\,a\,b^3}{6}-9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-40\,A\,a^4-\frac{104\,A\,b^4}{5}-24\,C\,a^4-\frac{424\,C\,b^4}{35}-144\,A\,a^2\,b^2-\frac{624\,C\,a^2\,b^2}{5}-\frac{416\,B\,a\,b^3}{5}-96\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(30\,A\,a^4+\frac{226\,A\,b^4}{15}+5\,B\,a^4+\frac{85\,B\,b^4}{24}+\frac{58\,C\,a^4}{3}+\frac{86\,C\,b^4}{5}+116\,A\,a^2\,b^2+\frac{27\,B\,a^2\,b^2}{2}+\frac{452\,C\,a^2\,b^2}{5}+9\,A\,a\,b^3+20\,A\,a^3\,b+\frac{904\,B\,a\,b^3}{15}+\frac{232\,B\,a^3\,b}{3}+\frac{85\,C\,a\,b^3}{6}+9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-12\,A\,a^4-\frac{20\,A\,b^4}{3}-4\,B\,a^4-\frac{7\,B\,b^4}{6}-\frac{28\,C\,a^4}{3}-4\,C\,b^4-56\,A\,a^2\,b^2-18\,B\,a^2\,b^2-40\,C\,a^2\,b^2-12\,A\,a\,b^3-16\,A\,a^3\,b-\frac{80\,B\,a\,b^3}{3}-\frac{112\,B\,a^3\,b}{3}-\frac{14\,C\,a\,b^3}{3}-12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+B\,a^4+\frac{11\,B\,b^4}{8}+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+\frac{15\,B\,a^2\,b^2}{2}+12\,C\,a^2\,b^2+5\,A\,a\,b^3+4\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,a^3\,b+\frac{11\,C\,a\,b^3}{2}+5\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((B*a^4)/2 + (5*B*b^4)/16 + (9*B*a^2*b^2)/4 + (3*A*a*b^3)/2 + 2*A*a^3*b + (5*C*a*b^3)/4 + (3*C*a^3*b)/2))/(2*B*a^4 + (5*B*b^4)/4 + 9*B*a^2*b^2 + 6*A*a*b^3 + 8*A*a^3*b + 5*C*a*b^3 + 6*C*a^3*b))*(B*a^4 + (5*B*b^4)/8 + (9*B*a^2*b^2)/2 + 3*A*a*b^3 + 4*A*a^3*b + (5*C*a*b^3)/2 + 3*C*a^3*b))/d - (tan(c/2 + (d*x)/2)^13*(2*A*a^4 + 2*A*b^4 - B*a^4 - (11*B*b^4)/8 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 - (15*B*a^2*b^2)/2 + 12*C*a^2*b^2 - 5*A*a*b^3 - 4*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b - (11*C*a*b^3)/2 - 5*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(12*A*a^4 + (20*A*b^4)/3 + 4*B*a^4 + (7*B*b^4)/6 + (28*C*a^4)/3 + 4*C*b^4 + 56*A*a^2*b^2 + 18*B*a^2*b^2 + 40*C*a^2*b^2 + 12*A*a*b^3 + 16*A*a^3*b + (80*B*a*b^3)/3 + (112*B*a^3*b)/3 + (14*C*a*b^3)/3 + 12*C*a^3*b) - tan(c/2 + (d*x)/2)^11*(12*A*a^4 + (20*A*b^4)/3 - 4*B*a^4 - (7*B*b^4)/6 + (28*C*a^4)/3 + 4*C*b^4 + 56*A*a^2*b^2 - 18*B*a^2*b^2 + 40*C*a^2*b^2 - 12*A*a*b^3 - 16*A*a^3*b + (80*B*a*b^3)/3 + (112*B*a^3*b)/3 - (14*C*a*b^3)/3 - 12*C*a^3*b) + tan(c/2 + (d*x)/2)^5*(30*A*a^4 + (226*A*b^4)/15 + 5*B*a^4 + (85*B*b^4)/24 + (58*C*a^4)/3 + (86*C*b^4)/5 + 116*A*a^2*b^2 + (27*B*a^2*b^2)/2 + (452*C*a^2*b^2)/5 + 9*A*a*b^3 + 20*A*a^3*b + (904*B*a*b^3)/15 + (232*B*a^3*b)/3 + (85*C*a*b^3)/6 + 9*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(30*A*a^4 + (226*A*b^4)/15 - 5*B*a^4 - (85*B*b^4)/24 + (58*C*a^4)/3 + (86*C*b^4)/5 + 116*A*a^2*b^2 - (27*B*a^2*b^2)/2 + (452*C*a^2*b^2)/5 - 9*A*a*b^3 - 20*A*a^3*b + (904*B*a*b^3)/15 + (232*B*a^3*b)/3 - (85*C*a*b^3)/6 - 9*C*a^3*b) - tan(c/2 + (d*x)/2)^7*(40*A*a^4 + (104*A*b^4)/5 + 24*C*a^4 + (424*C*b^4)/35 + 144*A*a^2*b^2 + (624*C*a^2*b^2)/5 + (416*B*a*b^3)/5 + 96*B*a^3*b) + tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + B*a^4 + (11*B*b^4)/8 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + (15*B*a^2*b^2)/2 + 12*C*a^2*b^2 + 5*A*a*b^3 + 4*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b + (11*C*a*b^3)/2 + 5*C*a^3*b))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
888,1,942,384,6.317987,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\left(\frac{5\,A\,b^4}{4}-2\,B\,a^4-2\,B\,b^4+C\,a^4+\frac{11\,C\,b^4}{8}+6\,A\,a^2\,b^2-12\,B\,a^2\,b^2+\frac{15\,C\,a^2\,b^2}{2}-8\,A\,a\,b^3-8\,A\,a^3\,b+5\,B\,a\,b^3+4\,B\,a^3\,b-8\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(10\,B\,a^4-\frac{7\,A\,b^4}{4}+\frac{14\,B\,b^4}{3}-3\,C\,a^4+\frac{5\,C\,b^4}{24}-18\,A\,a^2\,b^2+44\,B\,a^2\,b^2-\frac{21\,C\,a^2\,b^2}{2}+\frac{88\,A\,a\,b^3}{3}+40\,A\,a^3\,b-7\,B\,a\,b^3-12\,B\,a^3\,b+\frac{56\,C\,a\,b^3}{3}+\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b^4}{2}-20\,B\,a^4-\frac{52\,B\,b^4}{5}+2\,C\,a^4+\frac{15\,C\,b^4}{4}+12\,A\,a^2\,b^2-72\,B\,a^2\,b^2+3\,C\,a^2\,b^2-48\,A\,a\,b^3-80\,A\,a^3\,b+2\,B\,a\,b^3+8\,B\,a^3\,b-\frac{208\,C\,a\,b^3}{5}-48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{A\,b^4}{2}+20\,B\,a^4+\frac{52\,B\,b^4}{5}+2\,C\,a^4+\frac{15\,C\,b^4}{4}+12\,A\,a^2\,b^2+72\,B\,a^2\,b^2+3\,C\,a^2\,b^2+48\,A\,a\,b^3+80\,A\,a^3\,b+2\,B\,a\,b^3+8\,B\,a^3\,b+\frac{208\,C\,a\,b^3}{5}+48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,C\,b^4}{24}-10\,B\,a^4-\frac{14\,B\,b^4}{3}-3\,C\,a^4-\frac{7\,A\,b^4}{4}-18\,A\,a^2\,b^2-44\,B\,a^2\,b^2-\frac{21\,C\,a^2\,b^2}{2}-\frac{88\,A\,a\,b^3}{3}-40\,A\,a^3\,b-7\,B\,a\,b^3-12\,B\,a^3\,b-\frac{56\,C\,a\,b^3}{3}-\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,b^4}{4}+2\,B\,a^4+2\,B\,b^4+C\,a^4+\frac{11\,C\,b^4}{8}+6\,A\,a^2\,b^2+12\,B\,a^2\,b^2+\frac{15\,C\,a^2\,b^2}{2}+8\,A\,a\,b^3+8\,A\,a^3\,b+5\,B\,a\,b^3+4\,B\,a^3\,b+8\,C\,a\,b^3+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^4+\frac{3\,A\,b^4}{8}+\frac{C\,a^4}{2}+\frac{5\,C\,b^4}{16}+3\,A\,a^2\,b^2+\frac{9\,C\,a^2\,b^2}{4}+\frac{3\,B\,a\,b^3}{2}+2\,B\,a^3\,b\right)}{4\,A\,a^4+\frac{3\,A\,b^4}{2}+2\,C\,a^4+\frac{5\,C\,b^4}{4}+12\,A\,a^2\,b^2+9\,C\,a^2\,b^2+6\,B\,a\,b^3+8\,B\,a^3\,b}\right)\,\left(2\,A\,a^4+\frac{3\,A\,b^4}{4}+C\,a^4+\frac{5\,C\,b^4}{8}+6\,A\,a^2\,b^2+\frac{9\,C\,a^2\,b^2}{2}+3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*b^4)/4 + 2*B*a^4 + 2*B*b^4 + C*a^4 + (11*C*b^4)/8 + 6*A*a^2*b^2 + 12*B*a^2*b^2 + (15*C*a^2*b^2)/2 + 8*A*a*b^3 + 8*A*a^3*b + 5*B*a*b^3 + 4*B*a^3*b + 8*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^11*((5*A*b^4)/4 - 2*B*a^4 - 2*B*b^4 + C*a^4 + (11*C*b^4)/8 + 6*A*a^2*b^2 - 12*B*a^2*b^2 + (15*C*a^2*b^2)/2 - 8*A*a*b^3 - 8*A*a^3*b + 5*B*a*b^3 + 4*B*a^3*b - 8*C*a*b^3 - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^3*((7*A*b^4)/4 + 10*B*a^4 + (14*B*b^4)/3 + 3*C*a^4 - (5*C*b^4)/24 + 18*A*a^2*b^2 + 44*B*a^2*b^2 + (21*C*a^2*b^2)/2 + (88*A*a*b^3)/3 + 40*A*a^3*b + 7*B*a*b^3 + 12*B*a^3*b + (56*C*a*b^3)/3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^9*(10*B*a^4 - (7*A*b^4)/4 + (14*B*b^4)/3 - 3*C*a^4 + (5*C*b^4)/24 - 18*A*a^2*b^2 + 44*B*a^2*b^2 - (21*C*a^2*b^2)/2 + (88*A*a*b^3)/3 + 40*A*a^3*b - 7*B*a*b^3 - 12*B*a^3*b + (56*C*a*b^3)/3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^5*((A*b^4)/2 + 20*B*a^4 + (52*B*b^4)/5 + 2*C*a^4 + (15*C*b^4)/4 + 12*A*a^2*b^2 + 72*B*a^2*b^2 + 3*C*a^2*b^2 + 48*A*a*b^3 + 80*A*a^3*b + 2*B*a*b^3 + 8*B*a^3*b + (208*C*a*b^3)/5 + 48*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((A*b^4)/2 - 20*B*a^4 - (52*B*b^4)/5 + 2*C*a^4 + (15*C*b^4)/4 + 12*A*a^2*b^2 - 72*B*a^2*b^2 + 3*C*a^2*b^2 - 48*A*a*b^3 - 80*A*a^3*b + 2*B*a*b^3 + 8*B*a^3*b - (208*C*a*b^3)/5 - 48*C*a^3*b))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*(A*a^4 + (3*A*b^4)/8 + (C*a^4)/2 + (5*C*b^4)/16 + 3*A*a^2*b^2 + (9*C*a^2*b^2)/4 + (3*B*a*b^3)/2 + 2*B*a^3*b))/(4*A*a^4 + (3*A*b^4)/2 + 2*C*a^4 + (5*C*b^4)/4 + 12*A*a^2*b^2 + 9*C*a^2*b^2 + 6*B*a*b^3 + 8*B*a^3*b))*(2*A*a^4 + (3*A*b^4)/4 + C*a^4 + (5*C*b^4)/8 + 6*A*a^2*b^2 + (9*C*a^2*b^2)/2 + 3*B*a*b^3 + 4*B*a^3*b))/d","B"
889,1,4068,290,7.879467,"\text{Not used}","int((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)\,1{}\mathrm{i}+\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)-\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4+\frac{3\,B\,b^4}{8}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+4\,A\,a^3\,b+\frac{3\,C\,a\,b^3}{2}+2\,C\,a^3\,b\right)+64\,A\,B^2\,a^{12}-64\,A^2\,B\,a^{12}-256\,A^3\,a^{11}\,b+256\,A^3\,a^6\,b^6+1024\,A^3\,a^8\,b^4-128\,A^3\,a^9\,b^3+1024\,A^3\,a^{10}\,b^2+512\,A^2\,B\,a^{11}\,b-128\,A^2\,C\,a^{11}\,b+9\,A\,B^2\,a^4\,b^8+144\,A\,B^2\,a^6\,b^6+624\,A\,B^2\,a^8\,b^4+384\,A\,B^2\,a^{10}\,b^2+96\,A^2\,B\,a^5\,b^7+960\,A^2\,B\,a^7\,b^5-24\,A^2\,B\,a^8\,b^4+1792\,A^2\,B\,a^9\,b^3-192\,A^2\,B\,a^{10}\,b^2+144\,A\,C^2\,a^6\,b^6+384\,A\,C^2\,a^8\,b^4+256\,A\,C^2\,a^{10}\,b^2+384\,A^2\,C\,a^6\,b^6+1280\,A^2\,C\,a^8\,b^4-96\,A^2\,C\,a^9\,b^3+1024\,A^2\,C\,a^{10}\,b^2+256\,A\,B\,C\,a^{11}\,b+72\,A\,B\,C\,a^5\,b^7+672\,A\,B\,C\,a^7\,b^5+960\,A\,B\,C\,a^9\,b^3}\right)\,\left(B\,a^4\,2{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{4}+B\,a^2\,b^2\,6{}\mathrm{i}+A\,a\,b^3\,4{}\mathrm{i}+A\,a^3\,b\,8{}\mathrm{i}+C\,a\,b^3\,3{}\mathrm{i}+C\,a^3\,b\,4{}\mathrm{i}\right)}{d}-\frac{\left(2\,A\,b^4-\frac{5\,B\,b^4}{4}+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2-6\,B\,a^2\,b^2+12\,C\,a^2\,b^2-4\,A\,a\,b^3+8\,B\,a\,b^3+8\,B\,a^3\,b-5\,C\,a\,b^3-4\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B\,b^4}{2}-\frac{16\,A\,b^4}{3}-8\,C\,a^4-\frac{8\,C\,b^4}{3}-48\,A\,a^2\,b^2+12\,B\,a^2\,b^2-32\,C\,a^2\,b^2+8\,A\,a\,b^3-\frac{64\,B\,a\,b^3}{3}-32\,B\,a^3\,b+2\,C\,a\,b^3+8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b^4}{3}+12\,C\,a^4+\frac{116\,C\,b^4}{15}+72\,A\,a^2\,b^2+40\,C\,a^2\,b^2+\frac{80\,B\,a\,b^3}{3}+48\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,A\,b^4}{3}-\frac{B\,b^4}{2}-8\,C\,a^4-\frac{8\,C\,b^4}{3}-48\,A\,a^2\,b^2-12\,B\,a^2\,b^2-32\,C\,a^2\,b^2-8\,A\,a\,b^3-\frac{64\,B\,a\,b^3}{3}-32\,B\,a^3\,b-2\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b^4+\frac{5\,B\,b^4}{4}+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+6\,B\,a^2\,b^2+12\,C\,a^2\,b^2+4\,A\,a\,b^3+8\,B\,a\,b^3+8\,B\,a^3\,b+5\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{2\,A\,a^4\,\mathrm{atan}\left(\frac{A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)}{64\,A\,B^2\,a^{12}-64\,A^2\,B\,a^{12}-256\,A^3\,a^{11}\,b+256\,A^3\,a^6\,b^6+1024\,A^3\,a^8\,b^4-128\,A^3\,a^9\,b^3+1024\,A^3\,a^{10}\,b^2+512\,A^2\,B\,a^{11}\,b-128\,A^2\,C\,a^{11}\,b+9\,A\,B^2\,a^4\,b^8+144\,A\,B^2\,a^6\,b^6+624\,A\,B^2\,a^8\,b^4+384\,A\,B^2\,a^{10}\,b^2+96\,A^2\,B\,a^5\,b^7+960\,A^2\,B\,a^7\,b^5-24\,A^2\,B\,a^8\,b^4+1792\,A^2\,B\,a^9\,b^3-192\,A^2\,B\,a^{10}\,b^2+144\,A\,C^2\,a^6\,b^6+384\,A\,C^2\,a^8\,b^4+256\,A\,C^2\,a^{10}\,b^2+384\,A^2\,C\,a^6\,b^6+1280\,A^2\,C\,a^8\,b^4-96\,A^2\,C\,a^9\,b^3+1024\,A^2\,C\,a^{10}\,b^2+256\,A\,B\,C\,a^{11}\,b+72\,A\,B\,C\,a^5\,b^7+672\,A\,B\,C\,a^7\,b^5+960\,A\,B\,C\,a^9\,b^3+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)}{d}","Not used",1,"(atan(((tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + (B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b)*1i + (tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - (B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b)*1i)/((tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - (B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b) - (tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + (B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4 + (3*B*b^4)/8 + 3*B*a^2*b^2 + 2*A*a*b^3 + 4*A*a^3*b + (3*C*a*b^3)/2 + 2*C*a^3*b) + 64*A*B^2*a^12 - 64*A^2*B*a^12 - 256*A^3*a^11*b + 256*A^3*a^6*b^6 + 1024*A^3*a^8*b^4 - 128*A^3*a^9*b^3 + 1024*A^3*a^10*b^2 + 512*A^2*B*a^11*b - 128*A^2*C*a^11*b + 9*A*B^2*a^4*b^8 + 144*A*B^2*a^6*b^6 + 624*A*B^2*a^8*b^4 + 384*A*B^2*a^10*b^2 + 96*A^2*B*a^5*b^7 + 960*A^2*B*a^7*b^5 - 24*A^2*B*a^8*b^4 + 1792*A^2*B*a^9*b^3 - 192*A^2*B*a^10*b^2 + 144*A*C^2*a^6*b^6 + 384*A*C^2*a^8*b^4 + 256*A*C^2*a^10*b^2 + 384*A^2*C*a^6*b^6 + 1280*A^2*C*a^8*b^4 - 96*A^2*C*a^9*b^3 + 1024*A^2*C*a^10*b^2 + 256*A*B*C*a^11*b + 72*A*B*C*a^5*b^7 + 672*A*B*C*a^7*b^5 + 960*A*B*C*a^9*b^3))*(B*a^4*2i + (B*b^4*3i)/4 + B*a^2*b^2*6i + A*a*b^3*4i + A*a^3*b*8i + C*a*b^3*3i + C*a^3*b*4i))/d - (tan(c/2 + (d*x)/2)*(2*A*b^4 + (5*B*b^4)/4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 6*B*a^2*b^2 + 12*C*a^2*b^2 + 4*A*a*b^3 + 8*B*a*b^3 + 8*B*a^3*b + 5*C*a*b^3 + 4*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*A*b^4 - (5*B*b^4)/4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 - 6*B*a^2*b^2 + 12*C*a^2*b^2 - 4*A*a*b^3 + 8*B*a*b^3 + 8*B*a^3*b - 5*C*a*b^3 - 4*C*a^3*b) - tan(c/2 + (d*x)/2)^3*((16*A*b^4)/3 + (B*b^4)/2 + 8*C*a^4 + (8*C*b^4)/3 + 48*A*a^2*b^2 + 12*B*a^2*b^2 + 32*C*a^2*b^2 + 8*A*a*b^3 + (64*B*a*b^3)/3 + 32*B*a^3*b + 2*C*a*b^3 + 8*C*a^3*b) - tan(c/2 + (d*x)/2)^7*((16*A*b^4)/3 - (B*b^4)/2 + 8*C*a^4 + (8*C*b^4)/3 + 48*A*a^2*b^2 - 12*B*a^2*b^2 + 32*C*a^2*b^2 - 8*A*a*b^3 + (64*B*a*b^3)/3 + 32*B*a^3*b - 2*C*a*b^3 - 8*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((20*A*b^4)/3 + 12*C*a^4 + (116*C*b^4)/15 + 72*A*a^2*b^2 + 40*C*a^2*b^2 + (80*B*a*b^3)/3 + 48*B*a^3*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) + (2*A*a^4*atan((A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i) + A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i))/(64*A*B^2*a^12 - 64*A^2*B*a^12 - 256*A^3*a^11*b + A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i)*1i - A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i)*1i + 256*A^3*a^6*b^6 + 1024*A^3*a^8*b^4 - 128*A^3*a^9*b^3 + 1024*A^3*a^10*b^2 + 512*A^2*B*a^11*b - 128*A^2*C*a^11*b + 9*A*B^2*a^4*b^8 + 144*A*B^2*a^6*b^6 + 624*A*B^2*a^8*b^4 + 384*A*B^2*a^10*b^2 + 96*A^2*B*a^5*b^7 + 960*A^2*B*a^7*b^5 - 24*A^2*B*a^8*b^4 + 1792*A^2*B*a^9*b^3 - 192*A^2*B*a^10*b^2 + 144*A*C^2*a^6*b^6 + 384*A*C^2*a^8*b^4 + 256*A*C^2*a^10*b^2 + 384*A^2*C*a^6*b^6 + 1280*A^2*C*a^8*b^4 - 96*A^2*C*a^9*b^3 + 1024*A^2*C*a^10*b^2 + 256*A*B*C*a^11*b + 72*A*B*C*a^5*b^7 + 672*A*B*C*a^7*b^5 + 960*A*B*C*a^9*b^3)))/d","B"
890,1,4710,273,8.806385,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(2\,A\,a^4+A\,b^4-2\,B\,b^4+\frac{5\,C\,b^4}{4}-12\,B\,a^2\,b^2+6\,C\,a^2\,b^2-8\,A\,a\,b^3+4\,B\,a\,b^3-8\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{4\,B\,b^4}{3}-8\,A\,a^4+2\,C\,b^4+24\,B\,a^2\,b^2+16\,A\,a\,b^3+\frac{16\,C\,a\,b^3}{3}+16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,A\,a^4-2\,A\,b^4+\frac{3\,C\,b^4}{2}-12\,C\,a^2\,b^2-8\,B\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,C\,b^4-\frac{4\,B\,b^4}{3}-8\,A\,a^4-24\,B\,a^2\,b^2-16\,A\,a\,b^3-\frac{16\,C\,a\,b^3}{3}-16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+A\,b^4+2\,B\,b^4+\frac{5\,C\,b^4}{4}+12\,B\,a^2\,b^2+6\,C\,a^2\,b^2+8\,A\,a\,b^3+4\,B\,a\,b^3+8\,C\,a\,b^3+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)\,1{}\mathrm{i}}{64\,B\,C^2\,a^{12}-\left(\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)-\left(\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4}{2}+C\,a^4+\frac{3\,C\,b^4}{8}+6\,A\,a^2\,b^2+3\,C\,a^2\,b^2+2\,B\,a\,b^3+4\,B\,a^3\,b\right)-64\,B^2\,C\,a^{12}-256\,B^3\,a^{11}\,b+64\,A^3\,a^3\,b^9+1536\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+9216\,A^3\,a^7\,b^5-6144\,A^3\,a^8\,b^4+256\,B^3\,a^6\,b^6+1024\,B^3\,a^8\,b^4-128\,B^3\,a^9\,b^3+1024\,B^3\,a^{10}\,b^2+256\,A\,C^2\,a^{11}\,b+512\,B^2\,C\,a^{11}\,b+1152\,A\,B^2\,a^5\,b^7+5888\,A\,B^2\,a^7\,b^5-1056\,A\,B^2\,a^8\,b^4+7168\,A\,B^2\,a^9\,b^3-2432\,A\,B^2\,a^{10}\,b^2+528\,A^2\,B\,a^4\,b^8+7552\,A^2\,B\,a^6\,b^6-2304\,A^2\,B\,a^7\,b^5+14592\,A^2\,B\,a^8\,b^4-7168\,A^2\,B\,a^9\,b^3+36\,A\,C^2\,a^3\,b^9+576\,A\,C^2\,a^5\,b^7+2496\,A\,C^2\,a^7\,b^5+1536\,A\,C^2\,a^9\,b^3+96\,A^2\,C\,a^3\,b^9+1920\,A^2\,C\,a^5\,b^7-384\,A^2\,C\,a^6\,b^6+9472\,A^2\,C\,a^7\,b^5-3072\,A^2\,C\,a^8\,b^4+3072\,A^2\,C\,a^9\,b^3-1024\,A^2\,C\,a^{10}\,b^2+9\,B\,C^2\,a^4\,b^8+144\,B\,C^2\,a^6\,b^6+624\,B\,C^2\,a^8\,b^4+384\,B\,C^2\,a^{10}\,b^2+96\,B^2\,C\,a^5\,b^7+960\,B^2\,C\,a^7\,b^5-24\,B^2\,C\,a^8\,b^4+1792\,B^2\,C\,a^9\,b^3-192\,B^2\,C\,a^{10}\,b^2-512\,A\,B\,C\,a^{11}\,b+408\,A\,B\,C\,a^4\,b^8+4320\,A\,B\,C\,a^6\,b^6-192\,A\,B\,C\,a^7\,b^5+9536\,A\,B\,C\,a^8\,b^4-1536\,A\,B\,C\,a^9\,b^3+2816\,A\,B\,C\,a^{10}\,b^2}\right)\,\left(A\,b^4\,1{}\mathrm{i}+C\,a^4\,2{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{4}+A\,a^2\,b^2\,12{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,8{}\mathrm{i}\right)}{d}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)-a^3\,\left(4\,A\,b+B\,a\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}\right)\,\left(4\,A\,b+B\,a\right)+a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)+a^3\,\left(4\,A\,b+B\,a\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}\right)\,\left(4\,A\,b+B\,a\right)}{64\,B\,C^2\,a^{12}-64\,B^2\,C\,a^{12}-256\,B^3\,a^{11}\,b+64\,A^3\,a^3\,b^9+1536\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+9216\,A^3\,a^7\,b^5-6144\,A^3\,a^8\,b^4+256\,B^3\,a^6\,b^6+1024\,B^3\,a^8\,b^4-128\,B^3\,a^9\,b^3+1024\,B^3\,a^{10}\,b^2+256\,A\,C^2\,a^{11}\,b+512\,B^2\,C\,a^{11}\,b+1152\,A\,B^2\,a^5\,b^7+5888\,A\,B^2\,a^7\,b^5-1056\,A\,B^2\,a^8\,b^4+7168\,A\,B^2\,a^9\,b^3-2432\,A\,B^2\,a^{10}\,b^2+528\,A^2\,B\,a^4\,b^8+7552\,A^2\,B\,a^6\,b^6-2304\,A^2\,B\,a^7\,b^5+14592\,A^2\,B\,a^8\,b^4-7168\,A^2\,B\,a^9\,b^3+36\,A\,C^2\,a^3\,b^9+576\,A\,C^2\,a^5\,b^7+2496\,A\,C^2\,a^7\,b^5+1536\,A\,C^2\,a^9\,b^3+96\,A^2\,C\,a^3\,b^9+1920\,A^2\,C\,a^5\,b^7-384\,A^2\,C\,a^6\,b^6+9472\,A^2\,C\,a^7\,b^5-3072\,A^2\,C\,a^8\,b^4+3072\,A^2\,C\,a^9\,b^3-1024\,A^2\,C\,a^{10}\,b^2+9\,B\,C^2\,a^4\,b^8+144\,B\,C^2\,a^6\,b^6+624\,B\,C^2\,a^8\,b^4+384\,B\,C^2\,a^{10}\,b^2+96\,B^2\,C\,a^5\,b^7+960\,B^2\,C\,a^7\,b^5-24\,B^2\,C\,a^8\,b^4+1792\,B^2\,C\,a^9\,b^3-192\,B^2\,C\,a^{10}\,b^2-512\,A\,B\,C\,a^{11}\,b+408\,A\,B\,C\,a^4\,b^8+4320\,A\,B\,C\,a^6\,b^6-192\,A\,B\,C\,a^7\,b^5+9536\,A\,B\,C\,a^8\,b^4-1536\,A\,B\,C\,a^9\,b^3+2816\,A\,B\,C\,a^{10}\,b^2+a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)-a^3\,\left(4\,A\,b+B\,a\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}\right)\,\left(4\,A\,b+B\,a\right)\,1{}\mathrm{i}-a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)+a^3\,\left(4\,A\,b+B\,a\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}\right)\,\left(4\,A\,b+B\,a\right)\,1{}\mathrm{i}}\right)\,\left(4\,A\,b+B\,a\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^4 + A*b^4 + 2*B*b^4 + (5*C*b^4)/4 + 12*B*a^2*b^2 + 6*C*a^2*b^2 + 8*A*a*b^3 + 4*B*a*b^3 + 8*C*a*b^3 + 8*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(8*A*a^4 + (4*B*b^4)/3 - 2*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*C*a*b^3)/3 + 16*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((4*B*b^4)/3 - 8*A*a^4 + 2*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*C*a*b^3)/3 + 16*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + A*b^4 - 2*B*b^4 + (5*C*b^4)/4 - 12*B*a^2*b^2 + 6*C*a^2*b^2 - 8*A*a*b^3 + 4*B*a*b^3 - 8*C*a*b^3 - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^5*(2*A*b^4 - 12*A*a^4 - (3*C*b^4)/2 + 12*C*a^2*b^2 + 8*B*a*b^3))/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (atan(((((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b)*1i - (((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b)*1i)/(64*B*C^2*a^12 - (((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b) - (((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4)/2 + C*a^4 + (3*C*b^4)/8 + 6*A*a^2*b^2 + 3*C*a^2*b^2 + 2*B*a*b^3 + 4*B*a^3*b) - 64*B^2*C*a^12 - 256*B^3*a^11*b + 64*A^3*a^3*b^9 + 1536*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 9216*A^3*a^7*b^5 - 6144*A^3*a^8*b^4 + 256*B^3*a^6*b^6 + 1024*B^3*a^8*b^4 - 128*B^3*a^9*b^3 + 1024*B^3*a^10*b^2 + 256*A*C^2*a^11*b + 512*B^2*C*a^11*b + 1152*A*B^2*a^5*b^7 + 5888*A*B^2*a^7*b^5 - 1056*A*B^2*a^8*b^4 + 7168*A*B^2*a^9*b^3 - 2432*A*B^2*a^10*b^2 + 528*A^2*B*a^4*b^8 + 7552*A^2*B*a^6*b^6 - 2304*A^2*B*a^7*b^5 + 14592*A^2*B*a^8*b^4 - 7168*A^2*B*a^9*b^3 + 36*A*C^2*a^3*b^9 + 576*A*C^2*a^5*b^7 + 2496*A*C^2*a^7*b^5 + 1536*A*C^2*a^9*b^3 + 96*A^2*C*a^3*b^9 + 1920*A^2*C*a^5*b^7 - 384*A^2*C*a^6*b^6 + 9472*A^2*C*a^7*b^5 - 3072*A^2*C*a^8*b^4 + 3072*A^2*C*a^9*b^3 - 1024*A^2*C*a^10*b^2 + 9*B*C^2*a^4*b^8 + 144*B*C^2*a^6*b^6 + 624*B*C^2*a^8*b^4 + 384*B*C^2*a^10*b^2 + 96*B^2*C*a^5*b^7 + 960*B^2*C*a^7*b^5 - 24*B^2*C*a^8*b^4 + 1792*B^2*C*a^9*b^3 - 192*B^2*C*a^10*b^2 - 512*A*B*C*a^11*b + 408*A*B*C*a^4*b^8 + 4320*A*B*C*a^6*b^6 - 192*A*B*C*a^7*b^5 + 9536*A*B*C*a^8*b^4 - 1536*A*B*C*a^9*b^3 + 2816*A*B*C*a^10*b^2))*(A*b^4*1i + C*a^4*2i + (C*b^4*3i)/4 + A*a^2*b^2*12i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*8i))/d + (2*a^3*atan((a^3*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3) - a^3*(4*A*b + B*a)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)*(4*A*b + B*a) + a^3*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3) + a^3*(4*A*b + B*a)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)*(4*A*b + B*a))/(64*B*C^2*a^12 - 64*B^2*C*a^12 - 256*B^3*a^11*b + 64*A^3*a^3*b^9 + 1536*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 9216*A^3*a^7*b^5 - 6144*A^3*a^8*b^4 + 256*B^3*a^6*b^6 + 1024*B^3*a^8*b^4 - 128*B^3*a^9*b^3 + 1024*B^3*a^10*b^2 + a^3*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3) - a^3*(4*A*b + B*a)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)*(4*A*b + B*a)*1i - a^3*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3) + a^3*(4*A*b + B*a)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)*(4*A*b + B*a)*1i + 256*A*C^2*a^11*b + 512*B^2*C*a^11*b + 1152*A*B^2*a^5*b^7 + 5888*A*B^2*a^7*b^5 - 1056*A*B^2*a^8*b^4 + 7168*A*B^2*a^9*b^3 - 2432*A*B^2*a^10*b^2 + 528*A^2*B*a^4*b^8 + 7552*A^2*B*a^6*b^6 - 2304*A^2*B*a^7*b^5 + 14592*A^2*B*a^8*b^4 - 7168*A^2*B*a^9*b^3 + 36*A*C^2*a^3*b^9 + 576*A*C^2*a^5*b^7 + 2496*A*C^2*a^7*b^5 + 1536*A*C^2*a^9*b^3 + 96*A^2*C*a^3*b^9 + 1920*A^2*C*a^5*b^7 - 384*A^2*C*a^6*b^6 + 9472*A^2*C*a^7*b^5 - 3072*A^2*C*a^8*b^4 + 3072*A^2*C*a^9*b^3 - 1024*A^2*C*a^10*b^2 + 9*B*C^2*a^4*b^8 + 144*B*C^2*a^6*b^6 + 624*B*C^2*a^8*b^4 + 384*B*C^2*a^10*b^2 + 96*B^2*C*a^5*b^7 + 960*B^2*C*a^7*b^5 - 24*B^2*C*a^8*b^4 + 1792*B^2*C*a^9*b^3 - 192*B^2*C*a^10*b^2 - 512*A*B*C*a^11*b + 408*A*B*C*a^4*b^8 + 4320*A*B*C*a^6*b^6 - 192*A*B*C*a^7*b^5 + 9536*A*B*C*a^8*b^4 - 1536*A*B*C*a^9*b^3 + 2816*A*B*C*a^10*b^2))*(4*A*b + B*a))/d","B"
891,1,4849,274,8.935762,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(2\,B\,a^4-2\,A\,b^4-A\,a^4+B\,b^4-2\,C\,b^4-12\,C\,a^2\,b^2+8\,A\,a^3\,b-8\,B\,a\,b^3+4\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(4\,A\,a^4-4\,B\,a^4+2\,B\,b^4-\frac{8\,C\,b^4}{3}-16\,A\,a^3\,b+8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(4\,A\,b^4-6\,A\,a^4-\frac{4\,C\,b^4}{3}+24\,C\,a^2\,b^2+16\,B\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A\,a^4+4\,B\,a^4-2\,B\,b^4-\frac{8\,C\,b^4}{3}+16\,A\,a^3\,b-8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-A\,a^4-2\,A\,b^4-2\,B\,a^4-B\,b^4-2\,C\,b^4-12\,C\,a^2\,b^2-8\,A\,a^3\,b-8\,B\,a\,b^3-4\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)\,1{}\mathrm{i}-\left(\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)\,1{}\mathrm{i}}{6144\,A^3\,a^4\,b^8-\left(\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)-256\,C^3\,a^{11}\,b-\left(\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{B\,b^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,C\,a\,b^3+4\,C\,a^3\,b\right)-9216\,A^3\,a^5\,b^7+512\,A^3\,a^6\,b^6-1536\,A^3\,a^7\,b^5-64\,A^3\,a^9\,b^3+64\,B^3\,a^3\,b^9+1536\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+9216\,B^3\,a^7\,b^5-6144\,B^3\,a^8\,b^4+256\,C^3\,a^6\,b^6+1024\,C^3\,a^8\,b^4-128\,C^3\,a^9\,b^3+1024\,C^3\,a^{10}\,b^2-256\,A\,C^2\,a^{11}\,b-64\,A^2\,C\,a^{11}\,b+96\,A\,B^2\,a^2\,b^{10}+3336\,A\,B^2\,a^4\,b^8-1536\,A\,B^2\,a^5\,b^7+26304\,A\,B^2\,a^6\,b^6-22656\,A\,B^2\,a^7\,b^5+1152\,A\,B^2\,a^8\,b^4-1536\,A\,B^2\,a^9\,b^3+1536\,A^2\,B\,a^3\,b^9-1152\,A^2\,B\,a^4\,b^8+22656\,A^2\,B\,a^5\,b^7-26304\,A^2\,B\,a^6\,b^6+1536\,A^2\,B\,a^7\,b^5-3336\,A^2\,B\,a^8\,b^4-96\,A^2\,B\,a^{10}\,b^2+1536\,A\,C^2\,a^4\,b^8+7296\,A\,C^2\,a^6\,b^6-1536\,A\,C^2\,a^7\,b^5+8704\,A\,C^2\,a^8\,b^4-3456\,A\,C^2\,a^9\,b^3+512\,A\,C^2\,a^{10}\,b^2+6144\,A^2\,C\,a^4\,b^8-4608\,A^2\,C\,a^5\,b^7+13824\,A^2\,C\,a^6\,b^6-13056\,A^2\,C\,a^7\,b^5+1024\,A^2\,C\,a^8\,b^4-1824\,A^2\,C\,a^9\,b^3+1152\,B\,C^2\,a^5\,b^7+5888\,B\,C^2\,a^7\,b^5-1056\,B\,C^2\,a^8\,b^4+7168\,B\,C^2\,a^9\,b^3-2432\,B\,C^2\,a^{10}\,b^2+528\,B^2\,C\,a^4\,b^8+7552\,B^2\,C\,a^6\,b^6-2304\,B^2\,C\,a^7\,b^5+14592\,B^2\,C\,a^8\,b^4-7168\,B^2\,C\,a^9\,b^3+768\,A\,B\,C\,a^3\,b^9+15168\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+30592\,A\,B\,C\,a^7\,b^5-19488\,A\,B\,C\,a^8\,b^4+1536\,A\,B\,C\,a^9\,b^3-1408\,A\,B\,C\,a^{10}\,b^2}\right)\,\left(B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,12{}\mathrm{i}+A\,a\,b^3\,8{}\mathrm{i}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,8{}\mathrm{i}\right)}{d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)}{2}+\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)}{2}}{6144\,A^3\,a^4\,b^8-256\,C^3\,a^{11}\,b-9216\,A^3\,a^5\,b^7+512\,A^3\,a^6\,b^6-1536\,A^3\,a^7\,b^5-64\,A^3\,a^9\,b^3+64\,B^3\,a^3\,b^9+1536\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+9216\,B^3\,a^7\,b^5-6144\,B^3\,a^8\,b^4+256\,C^3\,a^6\,b^6+1024\,C^3\,a^8\,b^4-128\,C^3\,a^9\,b^3+1024\,C^3\,a^{10}\,b^2-256\,A\,C^2\,a^{11}\,b-64\,A^2\,C\,a^{11}\,b+96\,A\,B^2\,a^2\,b^{10}+3336\,A\,B^2\,a^4\,b^8-1536\,A\,B^2\,a^5\,b^7+26304\,A\,B^2\,a^6\,b^6-22656\,A\,B^2\,a^7\,b^5+1152\,A\,B^2\,a^8\,b^4-1536\,A\,B^2\,a^9\,b^3+1536\,A^2\,B\,a^3\,b^9-1152\,A^2\,B\,a^4\,b^8+22656\,A^2\,B\,a^5\,b^7-26304\,A^2\,B\,a^6\,b^6+1536\,A^2\,B\,a^7\,b^5-3336\,A^2\,B\,a^8\,b^4-96\,A^2\,B\,a^{10}\,b^2+1536\,A\,C^2\,a^4\,b^8+7296\,A\,C^2\,a^6\,b^6-1536\,A\,C^2\,a^7\,b^5+8704\,A\,C^2\,a^8\,b^4-3456\,A\,C^2\,a^9\,b^3+512\,A\,C^2\,a^{10}\,b^2+6144\,A^2\,C\,a^4\,b^8-4608\,A^2\,C\,a^5\,b^7+13824\,A^2\,C\,a^6\,b^6-13056\,A^2\,C\,a^7\,b^5+1024\,A^2\,C\,a^8\,b^4-1824\,A^2\,C\,a^9\,b^3+1152\,B\,C^2\,a^5\,b^7+5888\,B\,C^2\,a^7\,b^5-1056\,B\,C^2\,a^8\,b^4+7168\,B\,C^2\,a^9\,b^3-2432\,B\,C^2\,a^{10}\,b^2+528\,B^2\,C\,a^4\,b^8+7552\,B^2\,C\,a^6\,b^6-2304\,B^2\,C\,a^7\,b^5+14592\,B^2\,C\,a^8\,b^4-7168\,B^2\,C\,a^9\,b^3+768\,A\,B\,C\,a^3\,b^9+15168\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+30592\,A\,B\,C\,a^7\,b^5-19488\,A\,B\,C\,a^8\,b^4+1536\,A\,B\,C\,a^9\,b^3-1408\,A\,B\,C\,a^{10}\,b^2+\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+\frac{a^2\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)\,1{}\mathrm{i}}{2}}\right)\,\left(A\,a^2+12\,A\,b^2+2\,C\,a^2+8\,B\,a\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(4*A*a^4 + 4*B*a^4 - 2*B*b^4 - (8*C*b^4)/3 + 16*A*a^3*b - 8*C*a*b^3) + tan(c/2 + (d*x)/2)^7*(4*A*a^4 - 4*B*a^4 + 2*B*b^4 - (8*C*b^4)/3 - 16*A*a^3*b + 8*C*a*b^3) - tan(c/2 + (d*x)/2)^9*(A*a^4 + 2*A*b^4 - 2*B*a^4 - B*b^4 + 2*C*b^4 + 12*C*a^2*b^2 - 8*A*a^3*b + 8*B*a*b^3 - 4*C*a*b^3) - tan(c/2 + (d*x)/2)*(A*a^4 + 2*A*b^4 + 2*B*a^4 + B*b^4 + 2*C*b^4 + 12*C*a^2*b^2 + 8*A*a^3*b + 8*B*a*b^3 + 4*C*a*b^3) + tan(c/2 + (d*x)/2)^5*(4*A*b^4 - 6*A*a^4 - (4*C*b^4)/3 + 24*C*a^2*b^2 + 16*B*a*b^3))/(d*(tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) + (atan(((((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b)*1i - (((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b)*1i)/(6144*A^3*a^4*b^8 - (((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b) - 256*C^3*a^11*b - (((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*b^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*C*a*b^3 + 4*C*a^3*b) - 9216*A^3*a^5*b^7 + 512*A^3*a^6*b^6 - 1536*A^3*a^7*b^5 - 64*A^3*a^9*b^3 + 64*B^3*a^3*b^9 + 1536*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 9216*B^3*a^7*b^5 - 6144*B^3*a^8*b^4 + 256*C^3*a^6*b^6 + 1024*C^3*a^8*b^4 - 128*C^3*a^9*b^3 + 1024*C^3*a^10*b^2 - 256*A*C^2*a^11*b - 64*A^2*C*a^11*b + 96*A*B^2*a^2*b^10 + 3336*A*B^2*a^4*b^8 - 1536*A*B^2*a^5*b^7 + 26304*A*B^2*a^6*b^6 - 22656*A*B^2*a^7*b^5 + 1152*A*B^2*a^8*b^4 - 1536*A*B^2*a^9*b^3 + 1536*A^2*B*a^3*b^9 - 1152*A^2*B*a^4*b^8 + 22656*A^2*B*a^5*b^7 - 26304*A^2*B*a^6*b^6 + 1536*A^2*B*a^7*b^5 - 3336*A^2*B*a^8*b^4 - 96*A^2*B*a^10*b^2 + 1536*A*C^2*a^4*b^8 + 7296*A*C^2*a^6*b^6 - 1536*A*C^2*a^7*b^5 + 8704*A*C^2*a^8*b^4 - 3456*A*C^2*a^9*b^3 + 512*A*C^2*a^10*b^2 + 6144*A^2*C*a^4*b^8 - 4608*A^2*C*a^5*b^7 + 13824*A^2*C*a^6*b^6 - 13056*A^2*C*a^7*b^5 + 1024*A^2*C*a^8*b^4 - 1824*A^2*C*a^9*b^3 + 1152*B*C^2*a^5*b^7 + 5888*B*C^2*a^7*b^5 - 1056*B*C^2*a^8*b^4 + 7168*B*C^2*a^9*b^3 - 2432*B*C^2*a^10*b^2 + 528*B^2*C*a^4*b^8 + 7552*B^2*C*a^6*b^6 - 2304*B^2*C*a^7*b^5 + 14592*B^2*C*a^8*b^4 - 7168*B^2*C*a^9*b^3 + 768*A*B*C*a^3*b^9 + 15168*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 30592*A*B*C*a^7*b^5 - 19488*A*B*C*a^8*b^4 + 1536*A*B*C*a^9*b^3 - 1408*A*B*C*a^10*b^2))*(B*b^4*1i + B*a^2*b^2*12i + A*a*b^3*8i + C*a*b^3*4i + C*a^3*b*8i))/d + (a^2*atan(((a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b))/2 + (a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b))/2)/((a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b)*1i)/2 - 256*C^3*a^11*b - (a^2*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (a^2*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b)*1i)/2 + 6144*A^3*a^4*b^8 - 9216*A^3*a^5*b^7 + 512*A^3*a^6*b^6 - 1536*A^3*a^7*b^5 - 64*A^3*a^9*b^3 + 64*B^3*a^3*b^9 + 1536*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 9216*B^3*a^7*b^5 - 6144*B^3*a^8*b^4 + 256*C^3*a^6*b^6 + 1024*C^3*a^8*b^4 - 128*C^3*a^9*b^3 + 1024*C^3*a^10*b^2 - 256*A*C^2*a^11*b - 64*A^2*C*a^11*b + 96*A*B^2*a^2*b^10 + 3336*A*B^2*a^4*b^8 - 1536*A*B^2*a^5*b^7 + 26304*A*B^2*a^6*b^6 - 22656*A*B^2*a^7*b^5 + 1152*A*B^2*a^8*b^4 - 1536*A*B^2*a^9*b^3 + 1536*A^2*B*a^3*b^9 - 1152*A^2*B*a^4*b^8 + 22656*A^2*B*a^5*b^7 - 26304*A^2*B*a^6*b^6 + 1536*A^2*B*a^7*b^5 - 3336*A^2*B*a^8*b^4 - 96*A^2*B*a^10*b^2 + 1536*A*C^2*a^4*b^8 + 7296*A*C^2*a^6*b^6 - 1536*A*C^2*a^7*b^5 + 8704*A*C^2*a^8*b^4 - 3456*A*C^2*a^9*b^3 + 512*A*C^2*a^10*b^2 + 6144*A^2*C*a^4*b^8 - 4608*A^2*C*a^5*b^7 + 13824*A^2*C*a^6*b^6 - 13056*A^2*C*a^7*b^5 + 1024*A^2*C*a^8*b^4 - 1824*A^2*C*a^9*b^3 + 1152*B*C^2*a^5*b^7 + 5888*B*C^2*a^7*b^5 - 1056*B*C^2*a^8*b^4 + 7168*B*C^2*a^9*b^3 - 2432*B*C^2*a^10*b^2 + 528*B^2*C*a^4*b^8 + 7552*B^2*C*a^6*b^6 - 2304*B^2*C*a^7*b^5 + 14592*B^2*C*a^8*b^4 - 7168*B^2*C*a^9*b^3 + 768*A*B*C*a^3*b^9 + 15168*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 30592*A*B*C*a^7*b^5 - 19488*A*B*C*a^8*b^4 + 1536*A*B*C*a^9*b^3 - 1408*A*B*C*a^10*b^2))*(A*a^2 + 12*A*b^2 + 2*C*a^2 + 8*B*a*b))/d","B"
892,1,4839,303,8.386753,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","-\frac{\left(B\,a^4-2\,A\,a^4+2\,B\,b^4-2\,C\,a^4-C\,b^4-12\,A\,a^2\,b^2+4\,A\,a^3\,b-8\,B\,a^3\,b+8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^4}{3}-2\,B\,a^4+4\,B\,b^4-4\,C\,b^4-8\,A\,a^3\,b+16\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(4\,C\,a^4-\frac{4\,A\,a^4}{3}-6\,C\,b^4+24\,A\,a^2\,b^2+16\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^4}{3}+2\,B\,a^4-4\,B\,b^4-4\,C\,b^4+8\,A\,a^3\,b-16\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,A\,a^4-B\,a^4-2\,B\,b^4-2\,C\,a^4-C\,b^4-12\,A\,a^2\,b^2-4\,A\,a^3\,b-8\,B\,a^3\,b-8\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)\,1{}\mathrm{i}-\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)\,1{}\mathrm{i}}{\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)+\left(\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(A\,b^4+\frac{C\,b^4}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3\right)-256\,A^3\,a\,b^{11}+1024\,A^3\,a^2\,b^{10}-128\,A^3\,a^3\,b^9+1024\,A^3\,a^4\,b^8+256\,A^3\,a^6\,b^6-6144\,B^3\,a^4\,b^8+9216\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+1536\,B^3\,a^7\,b^5+64\,B^3\,a^9\,b^3-64\,C^3\,a^3\,b^9-1536\,C^3\,a^5\,b^7+512\,C^3\,a^6\,b^6-9216\,C^3\,a^7\,b^5+6144\,C^3\,a^8\,b^4-64\,A\,C^2\,a\,b^{11}-256\,A^2\,C\,a\,b^{11}-7168\,A\,B^2\,a^3\,b^9+14592\,A\,B^2\,a^4\,b^8-2304\,A\,B^2\,a^5\,b^7+7552\,A\,B^2\,a^6\,b^6+528\,A\,B^2\,a^8\,b^4-2432\,A^2\,B\,a^2\,b^{10}+7168\,A^2\,B\,a^3\,b^9-1056\,A^2\,B\,a^4\,b^8+5888\,A^2\,B\,a^5\,b^7+1152\,A^2\,B\,a^7\,b^5-1824\,A\,C^2\,a^3\,b^9+1024\,A\,C^2\,a^4\,b^8-13056\,A\,C^2\,a^5\,b^7+13824\,A\,C^2\,a^6\,b^6-4608\,A\,C^2\,a^7\,b^5+6144\,A\,C^2\,a^8\,b^4+512\,A^2\,C\,a^2\,b^{10}-3456\,A^2\,C\,a^3\,b^9+8704\,A^2\,C\,a^4\,b^8-1536\,A^2\,C\,a^5\,b^7+7296\,A^2\,C\,a^6\,b^6+1536\,A^2\,C\,a^8\,b^4-96\,B\,C^2\,a^2\,b^{10}-3336\,B\,C^2\,a^4\,b^8+1536\,B\,C^2\,a^5\,b^7-26304\,B\,C^2\,a^6\,b^6+22656\,B\,C^2\,a^7\,b^5-1152\,B\,C^2\,a^8\,b^4+1536\,B\,C^2\,a^9\,b^3-1536\,B^2\,C\,a^3\,b^9+1152\,B^2\,C\,a^4\,b^8-22656\,B^2\,C\,a^5\,b^7+26304\,B^2\,C\,a^6\,b^6-1536\,B^2\,C\,a^7\,b^5+3336\,B^2\,C\,a^8\,b^4+96\,B^2\,C\,a^{10}\,b^2-1408\,A\,B\,C\,a^2\,b^{10}+1536\,A\,B\,C\,a^3\,b^9-19488\,A\,B\,C\,a^4\,b^8+30592\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+15168\,A\,B\,C\,a^7\,b^5+768\,A\,B\,C\,a^9\,b^3}\right)\,\left(A\,b^4\,2{}\mathrm{i}+C\,b^4\,1{}\mathrm{i}+C\,a^2\,b^2\,12{}\mathrm{i}+B\,a\,b^3\,8{}\mathrm{i}\right)}{d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-\frac{a\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)}{2}+\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+\frac{a\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)}{2}}{1024\,A^3\,a^2\,b^{10}-256\,A^3\,a\,b^{11}-128\,A^3\,a^3\,b^9+1024\,A^3\,a^4\,b^8+256\,A^3\,a^6\,b^6-6144\,B^3\,a^4\,b^8+9216\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+1536\,B^3\,a^7\,b^5+64\,B^3\,a^9\,b^3-64\,C^3\,a^3\,b^9-1536\,C^3\,a^5\,b^7+512\,C^3\,a^6\,b^6-9216\,C^3\,a^7\,b^5+6144\,C^3\,a^8\,b^4-64\,A\,C^2\,a\,b^{11}-256\,A^2\,C\,a\,b^{11}-7168\,A\,B^2\,a^3\,b^9+14592\,A\,B^2\,a^4\,b^8-2304\,A\,B^2\,a^5\,b^7+7552\,A\,B^2\,a^6\,b^6+528\,A\,B^2\,a^8\,b^4-2432\,A^2\,B\,a^2\,b^{10}+7168\,A^2\,B\,a^3\,b^9-1056\,A^2\,B\,a^4\,b^8+5888\,A^2\,B\,a^5\,b^7+1152\,A^2\,B\,a^7\,b^5-1824\,A\,C^2\,a^3\,b^9+1024\,A\,C^2\,a^4\,b^8-13056\,A\,C^2\,a^5\,b^7+13824\,A\,C^2\,a^6\,b^6-4608\,A\,C^2\,a^7\,b^5+6144\,A\,C^2\,a^8\,b^4+512\,A^2\,C\,a^2\,b^{10}-3456\,A^2\,C\,a^3\,b^9+8704\,A^2\,C\,a^4\,b^8-1536\,A^2\,C\,a^5\,b^7+7296\,A^2\,C\,a^6\,b^6+1536\,A^2\,C\,a^8\,b^4-96\,B\,C^2\,a^2\,b^{10}-3336\,B\,C^2\,a^4\,b^8+1536\,B\,C^2\,a^5\,b^7-26304\,B\,C^2\,a^6\,b^6+22656\,B\,C^2\,a^7\,b^5-1152\,B\,C^2\,a^8\,b^4+1536\,B\,C^2\,a^9\,b^3-1536\,B^2\,C\,a^3\,b^9+1152\,B^2\,C\,a^4\,b^8-22656\,B^2\,C\,a^5\,b^7+26304\,B^2\,C\,a^6\,b^6-1536\,B^2\,C\,a^7\,b^5+3336\,B^2\,C\,a^8\,b^4+96\,B^2\,C\,a^{10}\,b^2-1408\,A\,B\,C\,a^2\,b^{10}+1536\,A\,B\,C\,a^3\,b^9-19488\,A\,B\,C\,a^4\,b^8+30592\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+15168\,A\,B\,C\,a^7\,b^5+768\,A\,B\,C\,a^9\,b^3-\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-\frac{a\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}+\frac{a\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+\frac{a\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}}\right)\,\left(8\,A\,b^3+B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,C\,a^2\,b\right)}{d}","Not used",1,"- (tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 + 2*B*a^4 - 4*B*b^4 - 4*C*b^4 + 8*A*a^3*b - 16*C*a*b^3) + tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 - 2*B*a^4 + 4*B*b^4 - 4*C*b^4 - 8*A*a^3*b + 16*C*a*b^3) - tan(c/2 + (d*x)/2)^9*(2*A*a^4 - B*a^4 - 2*B*b^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 - 4*A*a^3*b + 8*B*a^3*b - 8*C*a*b^3) - tan(c/2 + (d*x)/2)*(2*A*a^4 + B*a^4 + 2*B*b^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 + 4*A*a^3*b + 8*B*a^3*b + 8*C*a*b^3) + tan(c/2 + (d*x)/2)^5*(4*C*a^4 - (4*A*a^4)/3 - 6*C*b^4 + 24*A*a^2*b^2 + 16*B*a^3*b))/(d*(tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (atan((((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3)*1i - ((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3)*1i)/(((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3) + ((A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*(A*b^4 + (C*b^4)/2 + 6*C*a^2*b^2 + 4*B*a*b^3) - 256*A^3*a*b^11 + 1024*A^3*a^2*b^10 - 128*A^3*a^3*b^9 + 1024*A^3*a^4*b^8 + 256*A^3*a^6*b^6 - 6144*B^3*a^4*b^8 + 9216*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 1536*B^3*a^7*b^5 + 64*B^3*a^9*b^3 - 64*C^3*a^3*b^9 - 1536*C^3*a^5*b^7 + 512*C^3*a^6*b^6 - 9216*C^3*a^7*b^5 + 6144*C^3*a^8*b^4 - 64*A*C^2*a*b^11 - 256*A^2*C*a*b^11 - 7168*A*B^2*a^3*b^9 + 14592*A*B^2*a^4*b^8 - 2304*A*B^2*a^5*b^7 + 7552*A*B^2*a^6*b^6 + 528*A*B^2*a^8*b^4 - 2432*A^2*B*a^2*b^10 + 7168*A^2*B*a^3*b^9 - 1056*A^2*B*a^4*b^8 + 5888*A^2*B*a^5*b^7 + 1152*A^2*B*a^7*b^5 - 1824*A*C^2*a^3*b^9 + 1024*A*C^2*a^4*b^8 - 13056*A*C^2*a^5*b^7 + 13824*A*C^2*a^6*b^6 - 4608*A*C^2*a^7*b^5 + 6144*A*C^2*a^8*b^4 + 512*A^2*C*a^2*b^10 - 3456*A^2*C*a^3*b^9 + 8704*A^2*C*a^4*b^8 - 1536*A^2*C*a^5*b^7 + 7296*A^2*C*a^6*b^6 + 1536*A^2*C*a^8*b^4 - 96*B*C^2*a^2*b^10 - 3336*B*C^2*a^4*b^8 + 1536*B*C^2*a^5*b^7 - 26304*B*C^2*a^6*b^6 + 22656*B*C^2*a^7*b^5 - 1152*B*C^2*a^8*b^4 + 1536*B*C^2*a^9*b^3 - 1536*B^2*C*a^3*b^9 + 1152*B^2*C*a^4*b^8 - 22656*B^2*C*a^5*b^7 + 26304*B^2*C*a^6*b^6 - 1536*B^2*C*a^7*b^5 + 3336*B^2*C*a^8*b^4 + 96*B^2*C*a^10*b^2 - 1408*A*B*C*a^2*b^10 + 1536*A*B*C*a^3*b^9 - 19488*A*B*C*a^4*b^8 + 30592*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 15168*A*B*C*a^7*b^5 + 768*A*B*C*a^9*b^3))*(A*b^4*2i + C*b^4*1i + C*a^2*b^2*12i + B*a*b^3*8i))/d - (a*atan(((a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b))/2 + (a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b))/2)/(1024*A^3*a^2*b^10 - 256*A^3*a*b^11 - 128*A^3*a^3*b^9 + 1024*A^3*a^4*b^8 + 256*A^3*a^6*b^6 - 6144*B^3*a^4*b^8 + 9216*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 1536*B^3*a^7*b^5 + 64*B^3*a^9*b^3 - 64*C^3*a^3*b^9 - 1536*C^3*a^5*b^7 + 512*C^3*a^6*b^6 - 9216*C^3*a^7*b^5 + 6144*C^3*a^8*b^4 - (a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b)*1i)/2 + (a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b)*1i)/2 - 64*A*C^2*a*b^11 - 256*A^2*C*a*b^11 - 7168*A*B^2*a^3*b^9 + 14592*A*B^2*a^4*b^8 - 2304*A*B^2*a^5*b^7 + 7552*A*B^2*a^6*b^6 + 528*A*B^2*a^8*b^4 - 2432*A^2*B*a^2*b^10 + 7168*A^2*B*a^3*b^9 - 1056*A^2*B*a^4*b^8 + 5888*A^2*B*a^5*b^7 + 1152*A^2*B*a^7*b^5 - 1824*A*C^2*a^3*b^9 + 1024*A*C^2*a^4*b^8 - 13056*A*C^2*a^5*b^7 + 13824*A*C^2*a^6*b^6 - 4608*A*C^2*a^7*b^5 + 6144*A*C^2*a^8*b^4 + 512*A^2*C*a^2*b^10 - 3456*A^2*C*a^3*b^9 + 8704*A^2*C*a^4*b^8 - 1536*A^2*C*a^5*b^7 + 7296*A^2*C*a^6*b^6 + 1536*A^2*C*a^8*b^4 - 96*B*C^2*a^2*b^10 - 3336*B*C^2*a^4*b^8 + 1536*B*C^2*a^5*b^7 - 26304*B*C^2*a^6*b^6 + 22656*B*C^2*a^7*b^5 - 1152*B*C^2*a^8*b^4 + 1536*B*C^2*a^9*b^3 - 1536*B^2*C*a^3*b^9 + 1152*B^2*C*a^4*b^8 - 22656*B^2*C*a^5*b^7 + 26304*B^2*C*a^6*b^6 - 1536*B^2*C*a^7*b^5 + 3336*B^2*C*a^8*b^4 + 96*B^2*C*a^10*b^2 - 1408*A*B*C*a^2*b^10 + 1536*A*B*C*a^3*b^9 - 19488*A*B*C*a^4*b^8 + 30592*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 15168*A*B*C*a^7*b^5 + 768*A*B*C*a^9*b^3))*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2 + 8*C*a^2*b))/d","B"
893,1,4781,293,8.624183,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(\frac{5\,A\,a^4}{4}-2\,B\,a^4+C\,a^4+2\,C\,b^4+6\,A\,a^2\,b^2-12\,B\,a^2\,b^2-8\,A\,a\,b^3-8\,A\,a^3\,b+4\,B\,a^3\,b-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(8\,C\,b^4-\frac{4\,B\,a^4}{3}-2\,A\,a^4-24\,B\,a^2\,b^2-16\,A\,a\,b^3-\frac{16\,A\,a^3\,b}{3}-16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a^4}{2}-2\,C\,a^4+12\,C\,b^4-12\,A\,a^2\,b^2-8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{4\,B\,a^4}{3}-2\,A\,a^4+8\,C\,b^4+24\,B\,a^2\,b^2+16\,A\,a\,b^3+\frac{16\,A\,a^3\,b}{3}+16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a^4}{4}+2\,B\,a^4+C\,a^4+2\,C\,b^4+6\,A\,a^2\,b^2+12\,B\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b+4\,B\,a^3\,b+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(B\,b^4+4\,C\,a\,b^3\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(B\,b^4+4\,C\,a\,b^3\right)\,1{}\mathrm{i}-\left(\left(B\,b^4+4\,C\,a\,b^3\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(B\,b^4+4\,C\,a\,b^3\right)\,1{}\mathrm{i}}{\left(\left(B\,b^4+4\,C\,a\,b^3\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(B\,b^4+4\,C\,a\,b^3\right)+\left(\left(B\,b^4+4\,C\,a\,b^3\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(B\,b^4+4\,C\,a\,b^3\right)-64\,A\,B^2\,b^{12}+64\,A^2\,B\,b^{12}-256\,B^3\,a\,b^{11}+1024\,B^3\,a^2\,b^{10}-128\,B^3\,a^3\,b^9+1024\,B^3\,a^4\,b^8+256\,B^3\,a^6\,b^6-6144\,C^3\,a^4\,b^8+9216\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+1536\,C^3\,a^7\,b^5+64\,C^3\,a^9\,b^3+512\,A\,B^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}-192\,A\,B^2\,a^2\,b^{10}+1792\,A\,B^2\,a^3\,b^9-24\,A\,B^2\,a^4\,b^8+960\,A\,B^2\,a^5\,b^7+96\,A\,B^2\,a^7\,b^5+384\,A^2\,B\,a^2\,b^{10}+624\,A^2\,B\,a^4\,b^8+144\,A^2\,B\,a^6\,b^6+9\,A^2\,B\,a^8\,b^4-1024\,A\,C^2\,a^2\,b^{10}+3072\,A\,C^2\,a^3\,b^9-3072\,A\,C^2\,a^4\,b^8+9472\,A\,C^2\,a^5\,b^7-384\,A\,C^2\,a^6\,b^6+1920\,A\,C^2\,a^7\,b^5+96\,A\,C^2\,a^9\,b^3+1536\,A^2\,C\,a^3\,b^9+2496\,A^2\,C\,a^5\,b^7+576\,A^2\,C\,a^7\,b^5+36\,A^2\,C\,a^9\,b^3-7168\,B\,C^2\,a^3\,b^9+14592\,B\,C^2\,a^4\,b^8-2304\,B\,C^2\,a^5\,b^7+7552\,B\,C^2\,a^6\,b^6+528\,B\,C^2\,a^8\,b^4-2432\,B^2\,C\,a^2\,b^{10}+7168\,B^2\,C\,a^3\,b^9-1056\,B^2\,C\,a^4\,b^8+5888\,B^2\,C\,a^5\,b^7+1152\,B^2\,C\,a^7\,b^5-512\,A\,B\,C\,a\,b^{11}+2816\,A\,B\,C\,a^2\,b^{10}-1536\,A\,B\,C\,a^3\,b^9+9536\,A\,B\,C\,a^4\,b^8-192\,A\,B\,C\,a^5\,b^7+4320\,A\,B\,C\,a^6\,b^6+408\,A\,B\,C\,a^8\,b^4}\right)\,\left(2{}\mathrm{i}\,B\,b^4+8{}\mathrm{i}\,C\,a\,b^3\right)}{d}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)+\left(\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4\,3{}\mathrm{i}}{8}+A\,b^4\,1{}\mathrm{i}+\frac{C\,a^4\,1{}\mathrm{i}}{2}+A\,a^2\,b^2\,3{}\mathrm{i}+C\,a^2\,b^2\,6{}\mathrm{i}+B\,a\,b^3\,4{}\mathrm{i}+B\,a^3\,b\,2{}\mathrm{i}\right)-64\,A\,B^2\,b^{12}+64\,A^2\,B\,b^{12}-256\,B^3\,a\,b^{11}+1024\,B^3\,a^2\,b^{10}-128\,B^3\,a^3\,b^9+1024\,B^3\,a^4\,b^8+256\,B^3\,a^6\,b^6-6144\,C^3\,a^4\,b^8+9216\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+1536\,C^3\,a^7\,b^5+64\,C^3\,a^9\,b^3+512\,A\,B^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}-192\,A\,B^2\,a^2\,b^{10}+1792\,A\,B^2\,a^3\,b^9-24\,A\,B^2\,a^4\,b^8+960\,A\,B^2\,a^5\,b^7+96\,A\,B^2\,a^7\,b^5+384\,A^2\,B\,a^2\,b^{10}+624\,A^2\,B\,a^4\,b^8+144\,A^2\,B\,a^6\,b^6+9\,A^2\,B\,a^8\,b^4-1024\,A\,C^2\,a^2\,b^{10}+3072\,A\,C^2\,a^3\,b^9-3072\,A\,C^2\,a^4\,b^8+9472\,A\,C^2\,a^5\,b^7-384\,A\,C^2\,a^6\,b^6+1920\,A\,C^2\,a^7\,b^5+96\,A\,C^2\,a^9\,b^3+1536\,A^2\,C\,a^3\,b^9+2496\,A^2\,C\,a^5\,b^7+576\,A^2\,C\,a^7\,b^5+36\,A^2\,C\,a^9\,b^3-7168\,B\,C^2\,a^3\,b^9+14592\,B\,C^2\,a^4\,b^8-2304\,B\,C^2\,a^5\,b^7+7552\,B\,C^2\,a^6\,b^6+528\,B\,C^2\,a^8\,b^4-2432\,B^2\,C\,a^2\,b^{10}+7168\,B^2\,C\,a^3\,b^9-1056\,B^2\,C\,a^4\,b^8+5888\,B^2\,C\,a^5\,b^7+1152\,B^2\,C\,a^7\,b^5-512\,A\,B\,C\,a\,b^{11}+2816\,A\,B\,C\,a^2\,b^{10}-1536\,A\,B\,C\,a^3\,b^9+9536\,A\,B\,C\,a^4\,b^8-192\,A\,B\,C\,a^5\,b^7+4320\,A\,B\,C\,a^6\,b^6+408\,A\,B\,C\,a^8\,b^4}\right)\,\left(\frac{3\,A\,a^4}{4}+2\,A\,b^4+C\,a^4+6\,A\,a^2\,b^2+12\,C\,a^2\,b^2+8\,B\,a\,b^3+4\,B\,a^3\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*a^4)/4 + 2*B*a^4 + C*a^4 + 2*C*b^4 + 6*A*a^2*b^2 + 12*B*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b + 4*B*a^3*b + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^3*((4*B*a^4)/3 - 2*A*a^4 + 8*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*A*a^3*b)/3 + 16*C*a^3*b) - tan(c/2 + (d*x)/2)^7*(2*A*a^4 + (4*B*a^4)/3 - 8*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*A*a^3*b)/3 + 16*C*a^3*b) + tan(c/2 + (d*x)/2)^9*((5*A*a^4)/4 - 2*B*a^4 + C*a^4 + 2*C*b^4 + 6*A*a^2*b^2 - 12*B*a^2*b^2 - 8*A*a*b^3 - 8*A*a^3*b + 4*B*a^3*b - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^5*(2*C*a^4 - (3*A*a^4)/2 - 12*C*b^4 + 12*A*a^2*b^2 + 8*B*a^3*b))/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1)) - (atan((((B*b^4 + 4*C*a*b^3)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) + tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*b^4 + 4*C*a*b^3)*1i - ((B*b^4 + 4*C*a*b^3)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) - tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*b^4 + 4*C*a*b^3)*1i)/(((B*b^4 + 4*C*a*b^3)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) + tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*b^4 + 4*C*a*b^3) + ((B*b^4 + 4*C*a*b^3)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) - tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*b^4 + 4*C*a*b^3) - 64*A*B^2*b^12 + 64*A^2*B*b^12 - 256*B^3*a*b^11 + 1024*B^3*a^2*b^10 - 128*B^3*a^3*b^9 + 1024*B^3*a^4*b^8 + 256*B^3*a^6*b^6 - 6144*C^3*a^4*b^8 + 9216*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 1536*C^3*a^7*b^5 + 64*C^3*a^9*b^3 + 512*A*B^2*a*b^11 + 256*A^2*C*a*b^11 - 192*A*B^2*a^2*b^10 + 1792*A*B^2*a^3*b^9 - 24*A*B^2*a^4*b^8 + 960*A*B^2*a^5*b^7 + 96*A*B^2*a^7*b^5 + 384*A^2*B*a^2*b^10 + 624*A^2*B*a^4*b^8 + 144*A^2*B*a^6*b^6 + 9*A^2*B*a^8*b^4 - 1024*A*C^2*a^2*b^10 + 3072*A*C^2*a^3*b^9 - 3072*A*C^2*a^4*b^8 + 9472*A*C^2*a^5*b^7 - 384*A*C^2*a^6*b^6 + 1920*A*C^2*a^7*b^5 + 96*A*C^2*a^9*b^3 + 1536*A^2*C*a^3*b^9 + 2496*A^2*C*a^5*b^7 + 576*A^2*C*a^7*b^5 + 36*A^2*C*a^9*b^3 - 7168*B*C^2*a^3*b^9 + 14592*B*C^2*a^4*b^8 - 2304*B*C^2*a^5*b^7 + 7552*B*C^2*a^6*b^6 + 528*B*C^2*a^8*b^4 - 2432*B^2*C*a^2*b^10 + 7168*B^2*C*a^3*b^9 - 1056*B^2*C*a^4*b^8 + 5888*B^2*C*a^5*b^7 + 1152*B^2*C*a^7*b^5 - 512*A*B*C*a*b^11 + 2816*A*B*C*a^2*b^10 - 1536*A*B*C*a^3*b^9 + 9536*A*B*C*a^4*b^8 - 192*A*B*C*a^5*b^7 + 4320*A*B*C*a^6*b^6 + 408*A*B*C*a^8*b^4))*(B*b^4*2i + C*a*b^3*8i))/d + (atan(((((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) + tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i)*1i - (((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) - tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i)*1i)/((((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) + tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i) + (((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) - tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*a^4*3i)/8 + A*b^4*1i + (C*a^4*1i)/2 + A*a^2*b^2*3i + C*a^2*b^2*6i + B*a*b^3*4i + B*a^3*b*2i) - 64*A*B^2*b^12 + 64*A^2*B*b^12 - 256*B^3*a*b^11 + 1024*B^3*a^2*b^10 - 128*B^3*a^3*b^9 + 1024*B^3*a^4*b^8 + 256*B^3*a^6*b^6 - 6144*C^3*a^4*b^8 + 9216*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 1536*C^3*a^7*b^5 + 64*C^3*a^9*b^3 + 512*A*B^2*a*b^11 + 256*A^2*C*a*b^11 - 192*A*B^2*a^2*b^10 + 1792*A*B^2*a^3*b^9 - 24*A*B^2*a^4*b^8 + 960*A*B^2*a^5*b^7 + 96*A*B^2*a^7*b^5 + 384*A^2*B*a^2*b^10 + 624*A^2*B*a^4*b^8 + 144*A^2*B*a^6*b^6 + 9*A^2*B*a^8*b^4 - 1024*A*C^2*a^2*b^10 + 3072*A*C^2*a^3*b^9 - 3072*A*C^2*a^4*b^8 + 9472*A*C^2*a^5*b^7 - 384*A*C^2*a^6*b^6 + 1920*A*C^2*a^7*b^5 + 96*A*C^2*a^9*b^3 + 1536*A^2*C*a^3*b^9 + 2496*A^2*C*a^5*b^7 + 576*A^2*C*a^7*b^5 + 36*A^2*C*a^9*b^3 - 7168*B*C^2*a^3*b^9 + 14592*B*C^2*a^4*b^8 - 2304*B*C^2*a^5*b^7 + 7552*B*C^2*a^6*b^6 + 528*B*C^2*a^8*b^4 - 2432*B^2*C*a^2*b^10 + 7168*B^2*C*a^3*b^9 - 1056*B^2*C*a^4*b^8 + 5888*B^2*C*a^5*b^7 + 1152*B^2*C*a^7*b^5 - 512*A*B*C*a*b^11 + 2816*A*B*C*a^2*b^10 - 1536*A*B*C*a^3*b^9 + 9536*A*B*C*a^4*b^8 - 192*A*B*C*a^5*b^7 + 4320*A*B*C*a^6*b^6 + 408*A*B*C*a^8*b^4))*((3*A*a^4)/4 + 2*A*b^4 + C*a^4 + 6*A*a^2*b^2 + 12*C*a^2*b^2 + 8*B*a*b^3 + 4*B*a^3*b))/d","B"
894,1,4118,314,7.804346,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{\left(2\,A\,a^4+2\,A\,b^4-\frac{5\,B\,a^4}{4}+2\,C\,a^4+12\,A\,a^2\,b^2-6\,B\,a^2\,b^2+12\,C\,a^2\,b^2-4\,A\,a\,b^3-5\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,a^3\,b-4\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^4}{3}+8\,A\,b^4-\frac{B\,a^4}{2}+\frac{16\,C\,a^4}{3}+32\,A\,a^2\,b^2-12\,B\,a^2\,b^2+48\,C\,a^2\,b^2-8\,A\,a\,b^3-2\,A\,a^3\,b+32\,B\,a\,b^3+\frac{64\,B\,a^3\,b}{3}-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^4}{15}+12\,A\,b^4+\frac{20\,C\,a^4}{3}+40\,A\,a^2\,b^2+72\,C\,a^2\,b^2+48\,B\,a\,b^3+\frac{80\,B\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^4}{3}+8\,A\,b^4+\frac{B\,a^4}{2}+\frac{16\,C\,a^4}{3}+32\,A\,a^2\,b^2+12\,B\,a^2\,b^2+48\,C\,a^2\,b^2+8\,A\,a\,b^3+2\,A\,a^3\,b+32\,B\,a\,b^3+\frac{64\,B\,a^3\,b}{3}+8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+\frac{5\,B\,a^4}{4}+2\,C\,a^4+12\,A\,a^2\,b^2+6\,B\,a^2\,b^2+12\,C\,a^2\,b^2+4\,A\,a\,b^3+5\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,a^3\,b+4\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)\,1{}\mathrm{i}+\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)-\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{B\,a^4\,3{}\mathrm{i}}{8}+B\,b^4\,1{}\mathrm{i}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+\frac{A\,a^3\,b\,3{}\mathrm{i}}{2}+C\,a\,b^3\,4{}\mathrm{i}+C\,a^3\,b\,2{}\mathrm{i}\right)-64\,B\,C^2\,b^{12}+64\,B^2\,C\,b^{12}-256\,C^3\,a\,b^{11}+1024\,C^3\,a^2\,b^{10}-128\,C^3\,a^3\,b^9+1024\,C^3\,a^4\,b^8+256\,C^3\,a^6\,b^6-128\,A\,C^2\,a\,b^{11}+512\,B\,C^2\,a\,b^{11}+1024\,A\,C^2\,a^2\,b^{10}-96\,A\,C^2\,a^3\,b^9+1280\,A\,C^2\,a^4\,b^8+384\,A\,C^2\,a^6\,b^6+256\,A^2\,C\,a^2\,b^{10}+384\,A^2\,C\,a^4\,b^8+144\,A^2\,C\,a^6\,b^6-192\,B\,C^2\,a^2\,b^{10}+1792\,B\,C^2\,a^3\,b^9-24\,B\,C^2\,a^4\,b^8+960\,B\,C^2\,a^5\,b^7+96\,B\,C^2\,a^7\,b^5+384\,B^2\,C\,a^2\,b^{10}+624\,B^2\,C\,a^4\,b^8+144\,B^2\,C\,a^6\,b^6+9\,B^2\,C\,a^8\,b^4+256\,A\,B\,C\,a\,b^{11}+960\,A\,B\,C\,a^3\,b^9+672\,A\,B\,C\,a^5\,b^7+72\,A\,B\,C\,a^7\,b^5}\right)\,\left(\frac{3\,B\,a^4}{4}+2\,B\,b^4+6\,B\,a^2\,b^2+4\,A\,a\,b^3+3\,A\,a^3\,b+8\,C\,a\,b^3+4\,C\,a^3\,b\right)}{d}-\frac{C\,b^4\,\mathrm{atan}\left(\frac{C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}+C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}}{64\,B^2\,C\,b^{12}-64\,B\,C^2\,b^{12}-256\,C^3\,a\,b^{11}+C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)-C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)+1024\,C^3\,a^2\,b^{10}-128\,C^3\,a^3\,b^9+1024\,C^3\,a^4\,b^8+256\,C^3\,a^6\,b^6-128\,A\,C^2\,a\,b^{11}+512\,B\,C^2\,a\,b^{11}+1024\,A\,C^2\,a^2\,b^{10}-96\,A\,C^2\,a^3\,b^9+1280\,A\,C^2\,a^4\,b^8+384\,A\,C^2\,a^6\,b^6+256\,A^2\,C\,a^2\,b^{10}+384\,A^2\,C\,a^4\,b^8+144\,A^2\,C\,a^6\,b^6-192\,B\,C^2\,a^2\,b^{10}+1792\,B\,C^2\,a^3\,b^9-24\,B\,C^2\,a^4\,b^8+960\,B\,C^2\,a^5\,b^7+96\,B\,C^2\,a^7\,b^5+384\,B^2\,C\,a^2\,b^{10}+624\,B^2\,C\,a^4\,b^8+144\,B^2\,C\,a^6\,b^6+9\,B^2\,C\,a^8\,b^4+256\,A\,B\,C\,a\,b^{11}+960\,A\,B\,C\,a^3\,b^9+672\,A\,B\,C\,a^5\,b^7+72\,A\,B\,C\,a^7\,b^5}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + (5*B*a^4)/4 + 2*C*a^4 + 12*A*a^2*b^2 + 6*B*a^2*b^2 + 12*C*a^2*b^2 + 4*A*a*b^3 + 5*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b + 4*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + 2*A*b^4 - (5*B*a^4)/4 + 2*C*a^4 + 12*A*a^2*b^2 - 6*B*a^2*b^2 + 12*C*a^2*b^2 - 4*A*a*b^3 - 5*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b - 4*C*a^3*b) + tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 + 8*A*b^4 + (B*a^4)/2 + (16*C*a^4)/3 + 32*A*a^2*b^2 + 12*B*a^2*b^2 + 48*C*a^2*b^2 + 8*A*a*b^3 + 2*A*a^3*b + 32*B*a*b^3 + (64*B*a^3*b)/3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 + 8*A*b^4 - (B*a^4)/2 + (16*C*a^4)/3 + 32*A*a^2*b^2 - 12*B*a^2*b^2 + 48*C*a^2*b^2 - 8*A*a*b^3 - 2*A*a^3*b + 32*B*a*b^3 + (64*B*a^3*b)/3 - 8*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^4)/15 + 12*A*b^4 + (20*C*a^4)/3 + 40*A*a^2*b^2 + 72*C*a^2*b^2 + 48*B*a*b^3 + (80*B*a^3*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (atan(((tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + ((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i)*1i + (tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - ((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i)*1i)/((tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + ((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i) - (tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - ((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((B*a^4*3i)/8 + B*b^4*1i + B*a^2*b^2*3i + A*a*b^3*2i + (A*a^3*b*3i)/2 + C*a*b^3*4i + C*a^3*b*2i) - 64*B*C^2*b^12 + 64*B^2*C*b^12 - 256*C^3*a*b^11 + 1024*C^3*a^2*b^10 - 128*C^3*a^3*b^9 + 1024*C^3*a^4*b^8 + 256*C^3*a^6*b^6 - 128*A*C^2*a*b^11 + 512*B*C^2*a*b^11 + 1024*A*C^2*a^2*b^10 - 96*A*C^2*a^3*b^9 + 1280*A*C^2*a^4*b^8 + 384*A*C^2*a^6*b^6 + 256*A^2*C*a^2*b^10 + 384*A^2*C*a^4*b^8 + 144*A^2*C*a^6*b^6 - 192*B*C^2*a^2*b^10 + 1792*B*C^2*a^3*b^9 - 24*B*C^2*a^4*b^8 + 960*B*C^2*a^5*b^7 + 96*B*C^2*a^7*b^5 + 384*B^2*C*a^2*b^10 + 624*B^2*C*a^4*b^8 + 144*B^2*C*a^6*b^6 + 9*B^2*C*a^8*b^4 + 256*A*B*C*a*b^11 + 960*A*B*C*a^3*b^9 + 672*A*B*C*a^5*b^7 + 72*A*B*C*a^7*b^5))*((3*B*a^4)/4 + 2*B*b^4 + 6*B*a^2*b^2 + 4*A*a*b^3 + 3*A*a^3*b + 8*C*a*b^3 + 4*C*a^3*b))/d - (C*b^4*atan((C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*1i + C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*1i)/(64*B^2*C*b^12 - 64*B*C^2*b^12 - 256*C^3*a*b^11 + C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)) - C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)) + 1024*C^3*a^2*b^10 - 128*C^3*a^3*b^9 + 1024*C^3*a^4*b^8 + 256*C^3*a^6*b^6 - 128*A*C^2*a*b^11 + 512*B*C^2*a*b^11 + 1024*A*C^2*a^2*b^10 - 96*A*C^2*a^3*b^9 + 1280*A*C^2*a^4*b^8 + 384*A*C^2*a^6*b^6 + 256*A^2*C*a^2*b^10 + 384*A^2*C*a^4*b^8 + 144*A^2*C*a^6*b^6 - 192*B*C^2*a^2*b^10 + 1792*B*C^2*a^3*b^9 - 24*B*C^2*a^4*b^8 + 960*B*C^2*a^5*b^7 + 96*B*C^2*a^7*b^5 + 384*B^2*C*a^2*b^10 + 624*B^2*C*a^4*b^8 + 144*B^2*C*a^6*b^6 + 9*B^2*C*a^8*b^4 + 256*A*B*C*a*b^11 + 960*A*B*C*a^3*b^9 + 672*A*B*C*a^5*b^7 + 72*A*B*C*a^7*b^5))*2i)/d","B"
895,1,534,372,7.136087,"\text{Not used}","int(cos(c + d*x)^6*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{5\,A\,a^4\,x}{16}+\frac{A\,b^4\,x}{2}+\frac{3\,C\,a^4\,x}{8}+C\,b^4\,x+2\,B\,a\,b^3\,x+\frac{3\,B\,a^3\,b\,x}{2}+\frac{5\,B\,a^4\,\sin\left(c+d\,x\right)}{8\,d}+\frac{B\,b^4\,\sin\left(c+d\,x\right)}{d}+\frac{9\,A\,a^2\,b^2\,x}{4}+3\,C\,a^2\,b^2\,x+\frac{15\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{A\,a^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{5\,A\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{A\,a^3\,b\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{B\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{B\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{B\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{9\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{C\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{B\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{4\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(5*A*a^4*x)/16 + (A*b^4*x)/2 + (3*C*a^4*x)/8 + C*b^4*x + 2*B*a*b^3*x + (3*B*a^3*b*x)/2 + (5*B*a^4*sin(c + d*x))/(8*d) + (B*b^4*sin(c + d*x))/d + (9*A*a^2*b^2*x)/4 + 3*C*a^2*b^2*x + (15*A*a^4*sin(2*c + 2*d*x))/(64*d) + (3*A*a^4*sin(4*c + 4*d*x))/(64*d) + (A*a^4*sin(6*c + 6*d*x))/(192*d) + (A*b^4*sin(2*c + 2*d*x))/(4*d) + (5*B*a^4*sin(3*c + 3*d*x))/(48*d) + (B*a^4*sin(5*c + 5*d*x))/(80*d) + (C*a^4*sin(2*c + 2*d*x))/(4*d) + (C*a^4*sin(4*c + 4*d*x))/(32*d) + (A*a*b^3*sin(3*c + 3*d*x))/(3*d) + (5*A*a^3*b*sin(3*c + 3*d*x))/(12*d) + (A*a^3*b*sin(5*c + 5*d*x))/(20*d) + (B*a*b^3*sin(2*c + 2*d*x))/d + (B*a^3*b*sin(2*c + 2*d*x))/d + (B*a^3*b*sin(4*c + 4*d*x))/(8*d) + (9*B*a^2*b^2*sin(c + d*x))/(2*d) + (C*a^3*b*sin(3*c + 3*d*x))/(3*d) + (3*A*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*A*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (B*a^2*b^2*sin(3*c + 3*d*x))/(2*d) + (3*C*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*A*a*b^3*sin(c + d*x))/d + (5*A*a^3*b*sin(c + d*x))/(2*d) + (4*C*a*b^3*sin(c + d*x))/d + (3*C*a^3*b*sin(c + d*x))/d","B"
896,1,675,438,9.475309,"\text{Not used}","int(cos(c + d*x)^7*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{5\,B\,a^4\,x}{16}+\frac{B\,b^4\,x}{2}+\frac{3\,A\,a\,b^3\,x}{2}+\frac{5\,A\,a^3\,b\,x}{4}+2\,C\,a\,b^3\,x+\frac{3\,C\,a^3\,b\,x}{2}+\frac{35\,A\,a^4\,\sin\left(c+d\,x\right)}{64\,d}+\frac{3\,A\,b^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,C\,a^4\,\sin\left(c+d\,x\right)}{8\,d}+\frac{C\,b^4\,\sin\left(c+d\,x\right)}{d}+\frac{9\,B\,a^2\,b^2\,x}{4}+\frac{7\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{64\,d}+\frac{7\,A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{320\,d}+\frac{A\,a^4\,\sin\left(7\,c+7\,d\,x\right)}{448\,d}+\frac{15\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{A\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{B\,a^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{B\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{15\,A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{16\,d}+\frac{A\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{3\,A\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{A\,a^3\,b\,\sin\left(6\,c+6\,d\,x\right)}{48\,d}+\frac{15\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{5\,B\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a^3\,b\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{C\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{C\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{C\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{9\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{5\,A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{8\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{40\,d}+\frac{3\,B\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,B\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{C\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2\,d}+\frac{3\,B\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,B\,a^3\,b\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(5*B*a^4*x)/16 + (B*b^4*x)/2 + (3*A*a*b^3*x)/2 + (5*A*a^3*b*x)/4 + 2*C*a*b^3*x + (3*C*a^3*b*x)/2 + (35*A*a^4*sin(c + d*x))/(64*d) + (3*A*b^4*sin(c + d*x))/(4*d) + (5*C*a^4*sin(c + d*x))/(8*d) + (C*b^4*sin(c + d*x))/d + (9*B*a^2*b^2*x)/4 + (7*A*a^4*sin(3*c + 3*d*x))/(64*d) + (7*A*a^4*sin(5*c + 5*d*x))/(320*d) + (A*a^4*sin(7*c + 7*d*x))/(448*d) + (15*B*a^4*sin(2*c + 2*d*x))/(64*d) + (A*b^4*sin(3*c + 3*d*x))/(12*d) + (3*B*a^4*sin(4*c + 4*d*x))/(64*d) + (B*a^4*sin(6*c + 6*d*x))/(192*d) + (B*b^4*sin(2*c + 2*d*x))/(4*d) + (5*C*a^4*sin(3*c + 3*d*x))/(48*d) + (C*a^4*sin(5*c + 5*d*x))/(80*d) + (A*a*b^3*sin(2*c + 2*d*x))/d + (15*A*a^3*b*sin(2*c + 2*d*x))/(16*d) + (A*a*b^3*sin(4*c + 4*d*x))/(8*d) + (3*A*a^3*b*sin(4*c + 4*d*x))/(16*d) + (A*a^3*b*sin(6*c + 6*d*x))/(48*d) + (15*A*a^2*b^2*sin(c + d*x))/(4*d) + (B*a*b^3*sin(3*c + 3*d*x))/(3*d) + (5*B*a^3*b*sin(3*c + 3*d*x))/(12*d) + (B*a^3*b*sin(5*c + 5*d*x))/(20*d) + (C*a*b^3*sin(2*c + 2*d*x))/d + (C*a^3*b*sin(2*c + 2*d*x))/d + (C*a^3*b*sin(4*c + 4*d*x))/(8*d) + (9*C*a^2*b^2*sin(c + d*x))/(2*d) + (5*A*a^2*b^2*sin(3*c + 3*d*x))/(8*d) + (3*A*a^2*b^2*sin(5*c + 5*d*x))/(40*d) + (3*B*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*B*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (C*a^2*b^2*sin(3*c + 3*d*x))/(2*d) + (3*B*a*b^3*sin(c + d*x))/d + (5*B*a^3*b*sin(c + d*x))/(2*d)","B"
897,1,3157,214,6.699510,"\text{Not used}","int((a + b/cos(c + d*x))^3*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b),x)","\frac{\left(\frac{5\,C\,b^5}{4}-2\,B\,b^5-12\,B\,a^2\,b^3+2\,C\,a^2\,b^3+4\,C\,a^3\,b^2+4\,B\,a\,b^4-6\,C\,a\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{10\,B\,b^5}{3}+\frac{3\,C\,b^5}{4}+36\,B\,a^2\,b^3-2\,C\,a^2\,b^3-12\,C\,a^3\,b^2-4\,B\,a\,b^4+10\,C\,a\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,C\,b^5}{4}-\frac{10\,B\,b^5}{3}-36\,B\,a^2\,b^3-2\,C\,a^2\,b^3+12\,C\,a^3\,b^2-4\,B\,a\,b^4-10\,C\,a\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,b^5+\frac{5\,C\,b^5}{4}+12\,B\,a^2\,b^3+2\,C\,a^2\,b^3-4\,C\,a^3\,b^2+4\,B\,a\,b^4+6\,C\,a\,b^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)+\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\right)\,\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)\,1{}\mathrm{i}+\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)-\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\right)\,\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)+\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\right)\,\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)-\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)-\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\right)\,\left(-3\,C\,a^4\,b+4\,B\,a^3\,b^2+C\,a^2\,b^3+2\,B\,a\,b^4+\frac{3\,C\,b^5}{8}\right)-192\,C^3\,a^{14}\,b-256\,B^3\,a^6\,b^9-1024\,B^3\,a^8\,b^7+128\,B^3\,a^9\,b^6-1024\,B^3\,a^{10}\,b^5+256\,B^3\,a^{11}\,b^4+9\,C^3\,a^5\,b^{10}+48\,C^3\,a^7\,b^8-80\,C^3\,a^9\,b^6+24\,C^3\,a^{10}\,b^5-384\,C^3\,a^{11}\,b^4+64\,C^3\,a^{12}\,b^3+576\,C^3\,a^{13}\,b^2-9\,B\,C^2\,a^4\,b^{11}+48\,B\,C^2\,a^6\,b^9+528\,B\,C^2\,a^8\,b^7-48\,B\,C^2\,a^9\,b^6+128\,B\,C^2\,a^{10}\,b^5-2112\,B\,C^2\,a^{12}\,b^3+640\,B\,C^2\,a^{13}\,b^2-96\,B^2\,C\,a^5\,b^{10}-192\,B^2\,C\,a^7\,b^8+24\,B^2\,C\,a^8\,b^7+1280\,B^2\,C\,a^9\,b^6-192\,B^2\,C\,a^{10}\,b^5+2560\,B^2\,C\,a^{11}\,b^4-704\,B^2\,C\,a^{12}\,b^3}\right)\,\left(-6{}\mathrm{i}\,C\,a^4\,b+8{}\mathrm{i}\,B\,a^3\,b^2+2{}\mathrm{i}\,C\,a^2\,b^3+4{}\mathrm{i}\,B\,a\,b^4+\frac{3{}\mathrm{i}\,C\,b^5}{4}\right)}{d}-\frac{2\,a^4\,\mathrm{atan}\left(\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)-a^4\,\left(B\,b-C\,a\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b-C\,a\right)+a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)+a^4\,\left(B\,b-C\,a\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b-C\,a\right)}{128\,B^3\,a^9\,b^6-256\,B^3\,a^6\,b^9-1024\,B^3\,a^8\,b^7-192\,C^3\,a^{14}\,b-1024\,B^3\,a^{10}\,b^5+256\,B^3\,a^{11}\,b^4+9\,C^3\,a^5\,b^{10}+48\,C^3\,a^7\,b^8-80\,C^3\,a^9\,b^6+24\,C^3\,a^{10}\,b^5-384\,C^3\,a^{11}\,b^4+64\,C^3\,a^{12}\,b^3+576\,C^3\,a^{13}\,b^2-9\,B\,C^2\,a^4\,b^{11}+48\,B\,C^2\,a^6\,b^9+528\,B\,C^2\,a^8\,b^7-48\,B\,C^2\,a^9\,b^6+128\,B\,C^2\,a^{10}\,b^5-2112\,B\,C^2\,a^{12}\,b^3+640\,B\,C^2\,a^{13}\,b^2-96\,B^2\,C\,a^5\,b^{10}-192\,B^2\,C\,a^7\,b^8+24\,B^2\,C\,a^8\,b^7+1280\,B^2\,C\,a^9\,b^6-192\,B^2\,C\,a^{10}\,b^5+2560\,B^2\,C\,a^{11}\,b^4-704\,B^2\,C\,a^{12}\,b^3-a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)-a^4\,\left(B\,b-C\,a\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}+a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2+512\,B^2\,a^6\,b^4+512\,B^2\,a^4\,b^6+128\,B^2\,a^2\,b^8-64\,B\,C\,a^9\,b-768\,B\,C\,a^7\,b^3-128\,B\,C\,a^5\,b^5+224\,B\,C\,a^3\,b^7+48\,B\,C\,a\,b^9+32\,C^2\,a^{10}+288\,C^2\,a^8\,b^2-192\,C^2\,a^6\,b^4-40\,C^2\,a^4\,b^6+24\,C^2\,a^2\,b^8+\frac{9\,C^2\,b^{10}}{2}\right)+a^4\,\left(B\,b-C\,a\right)\,\left(12\,C\,b^5-32\,C\,a^5+128\,B\,a^3\,b^2+32\,C\,a^2\,b^3+64\,B\,a\,b^4+32\,B\,a^4\,b-96\,C\,a^4\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}\right)\,\left(B\,b-C\,a\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*B*b^5 + (5*C*b^5)/4 + 12*B*a^2*b^3 + 2*C*a^2*b^3 - 4*C*a^3*b^2 + 4*B*a*b^4 + 6*C*a*b^4) + tan(c/2 + (d*x)/2)^7*((5*C*b^5)/4 - 2*B*b^5 - 12*B*a^2*b^3 + 2*C*a^2*b^3 + 4*C*a^3*b^2 + 4*B*a*b^4 - 6*C*a*b^4) - tan(c/2 + (d*x)/2)^3*((10*B*b^5)/3 - (3*C*b^5)/4 + 36*B*a^2*b^3 + 2*C*a^2*b^3 - 12*C*a^3*b^2 + 4*B*a*b^4 + 10*C*a*b^4) + tan(c/2 + (d*x)/2)^5*((10*B*b^5)/3 + (3*C*b^5)/4 + 36*B*a^2*b^3 - 2*C*a^2*b^3 - 12*C*a^3*b^2 - 4*B*a*b^4 + 10*C*a*b^4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atan(((tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) + ((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b))*((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b)*1i + (tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) - ((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b))*((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b)*1i)/((tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) + ((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b))*((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b) - (tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) - ((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b))*((3*C*b^5)/8 + 4*B*a^3*b^2 + C*a^2*b^3 + 2*B*a*b^4 - 3*C*a^4*b) - 192*C^3*a^14*b - 256*B^3*a^6*b^9 - 1024*B^3*a^8*b^7 + 128*B^3*a^9*b^6 - 1024*B^3*a^10*b^5 + 256*B^3*a^11*b^4 + 9*C^3*a^5*b^10 + 48*C^3*a^7*b^8 - 80*C^3*a^9*b^6 + 24*C^3*a^10*b^5 - 384*C^3*a^11*b^4 + 64*C^3*a^12*b^3 + 576*C^3*a^13*b^2 - 9*B*C^2*a^4*b^11 + 48*B*C^2*a^6*b^9 + 528*B*C^2*a^8*b^7 - 48*B*C^2*a^9*b^6 + 128*B*C^2*a^10*b^5 - 2112*B*C^2*a^12*b^3 + 640*B*C^2*a^13*b^2 - 96*B^2*C*a^5*b^10 - 192*B^2*C*a^7*b^8 + 24*B^2*C*a^8*b^7 + 1280*B^2*C*a^9*b^6 - 192*B^2*C*a^10*b^5 + 2560*B^2*C*a^11*b^4 - 704*B^2*C*a^12*b^3))*((C*b^5*3i)/4 + B*a^3*b^2*8i + C*a^2*b^3*2i + B*a*b^4*4i - C*a^4*b*6i))/d - (2*a^4*atan((a^4*(tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) - a^4*(B*b - C*a)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b)*1i)*(B*b - C*a) + a^4*(tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) + a^4*(B*b - C*a)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b)*1i)*(B*b - C*a))/(128*B^3*a^9*b^6 - 256*B^3*a^6*b^9 - 1024*B^3*a^8*b^7 - 192*C^3*a^14*b - 1024*B^3*a^10*b^5 + 256*B^3*a^11*b^4 + 9*C^3*a^5*b^10 + 48*C^3*a^7*b^8 - 80*C^3*a^9*b^6 + 24*C^3*a^10*b^5 - 384*C^3*a^11*b^4 + 64*C^3*a^12*b^3 + 576*C^3*a^13*b^2 - a^4*(tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) - a^4*(B*b - C*a)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b)*1i)*(B*b - C*a)*1i + a^4*(tan(c/2 + (d*x)/2)*(32*C^2*a^10 + (9*C^2*b^10)/2 + 128*B^2*a^2*b^8 + 512*B^2*a^4*b^6 + 512*B^2*a^6*b^4 + 32*B^2*a^8*b^2 + 24*C^2*a^2*b^8 - 40*C^2*a^4*b^6 - 192*C^2*a^6*b^4 + 288*C^2*a^8*b^2 + 48*B*C*a*b^9 - 64*B*C*a^9*b + 224*B*C*a^3*b^7 - 128*B*C*a^5*b^5 - 768*B*C*a^7*b^3) + a^4*(B*b - C*a)*(12*C*b^5 - 32*C*a^5 + 128*B*a^3*b^2 + 32*C*a^2*b^3 + 64*B*a*b^4 + 32*B*a^4*b - 96*C*a^4*b)*1i)*(B*b - C*a)*1i - 9*B*C^2*a^4*b^11 + 48*B*C^2*a^6*b^9 + 528*B*C^2*a^8*b^7 - 48*B*C^2*a^9*b^6 + 128*B*C^2*a^10*b^5 - 2112*B*C^2*a^12*b^3 + 640*B*C^2*a^13*b^2 - 96*B^2*C*a^5*b^10 - 192*B^2*C*a^7*b^8 + 24*B^2*C*a^8*b^7 + 1280*B^2*C*a^9*b^6 - 192*B^2*C*a^10*b^5 + 2560*B^2*C*a^11*b^4 - 704*B^2*C*a^12*b^3))*(B*b - C*a))/d","B"
898,1,576,149,6.717976,"\text{Not used}","int((a + b/cos(c + d*x))^2*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b),x)","\frac{\frac{B\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{C\,b^4\,\sin\left(c+d\,x\right)}{2}+\frac{3\,B\,a\,b^3\,\sin\left(c+d\,x\right)}{4}-\frac{3\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{B\,b^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4}+\frac{3\,B\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}-\frac{C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{B\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{4}+\frac{B\,a^3\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{B\,a^2\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{2}-\frac{C\,a\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}+C\,a^3\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}-\frac{B\,a^2\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{2}+\frac{3\,B\,a^3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{C\,a\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}+C\,a^3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((B*b^4*sin(2*c + 2*d*x))/4 + (C*b^4*sin(3*c + 3*d*x))/6 + (C*b^4*sin(c + d*x))/2 + (3*B*a*b^3*sin(c + d*x))/4 - (3*C*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (B*b^4*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 + (3*B*a*b^3*sin(3*c + 3*d*x))/4 + (C*a*b^3*sin(2*c + 2*d*x))/2 - (C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (B*b^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/4 + (B*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (B*a^2*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2 - (C*a*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 + C*a^3*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i - (B*a^2*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/2 + (3*B*a^3*b*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (C*a*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 + C*a^3*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
899,1,221,97,5.396609,"\text{Not used}","int((a + b/cos(c + d*x))*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b),x)","\frac{\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2}-B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}-C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}\right)}{d}","Not used",1,"((B*b^3*sin(2*c + 2*d*x))/2 + (C*b^3*sin(c + d*x))/2 + (C*a*b^2*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*(C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2 - B*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i - C*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i))/d","B"
900,1,7016,215,14.382268,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^2-B\,b^2+2\,C\,a^2+2\,C\,b^2-2\,B\,a\,b+C\,a\,b\right)}{b^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^2+3\,C\,a^2+C\,b^2-3\,B\,a\,b\right)}{3\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^2+B\,b^2+2\,C\,a^2+2\,C\,b^2-2\,B\,a\,b-C\,a\,b\right)}{b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^{10}}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^4}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^{10}}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^4}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^2\,B\,a^6\,b^5+14\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+4\,A^2\,B\,a^3\,b^8+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,B^2\,a^7\,b^4-16\,A\,B^2\,a^6\,b^5+12\,A\,B^2\,a^5\,b^6-9\,A\,B^2\,a^4\,b^7+2\,A\,B^2\,a^3\,b^8-A\,B^2\,a^2\,b^9-24\,A\,B\,C\,a^8\,b^3+32\,A\,B\,C\,a^7\,b^4-24\,A\,B\,C\,a^6\,b^5+18\,A\,B\,C\,a^5\,b^6-4\,A\,B\,C\,a^4\,b^7+2\,A\,B\,C\,a^3\,b^8+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^{10}}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^4}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^{10}}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^4}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)}{b^4}}\right)\,\left(\frac{B\,b^3}{2}-C\,a^3-b^2\,\left(A\,a+\frac{C\,a}{2}\right)+B\,a^2\,b\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^2\,B\,a^6\,b^5+14\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+4\,A^2\,B\,a^3\,b^8+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,B^2\,a^7\,b^4-16\,A\,B^2\,a^6\,b^5+12\,A\,B^2\,a^5\,b^6-9\,A\,B^2\,a^4\,b^7+2\,A\,B^2\,a^3\,b^8-A\,B^2\,a^2\,b^9-24\,A\,B\,C\,a^8\,b^3+32\,A\,B\,C\,a^7\,b^4-24\,A\,B\,C\,a^6\,b^5+18\,A\,B\,C\,a^5\,b^6-4\,A\,B\,C\,a^4\,b^7+2\,A\,B\,C\,a^3\,b^8+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}-\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}+\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^5*(2*A*b^2 - B*b^2 + 2*C*a^2 + 2*C*b^2 - 2*B*a*b + C*a*b))/b^3 - (4*tan(c/2 + (d*x)/2)^3*(3*A*b^2 + 3*C*a^2 + C*b^2 - 3*B*a*b))/(3*b^3) + (tan(c/2 + (d*x)/2)*(2*A*b^2 + B*b^2 + 2*C*a^2 + 2*C*b^2 - 2*B*a*b - C*a*b))/b^3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1)) - (atan(((((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^10)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^4)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b)*1i)/b^4 + (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^10)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^4)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b)*1i)/b^4)/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b - A*B^2*a^2*b^9 + 2*A*B^2*a^3*b^8 - 9*A*B^2*a^4*b^7 + 12*A*B^2*a^5*b^6 - 16*A*B^2*a^6*b^5 + 12*A*B^2*a^7*b^4 + 4*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 14*A^2*B*a^5*b^6 - 12*A^2*B*a^6*b^5 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4 + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2 + 2*A*B*C*a^3*b^8 - 4*A*B*C*a^4*b^7 + 18*A*B*C*a^5*b^6 - 24*A*B*C*a^6*b^5 + 32*A*B*C*a^7*b^4 - 24*A*B*C*a^8*b^3))/b^9 - (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^10)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^4)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^4 + (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^10)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^4)*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b))/b^4))*((B*b^3)/2 - C*a^3 - b^2*(A*a + (C*a)/2) + B*a^2*b)*2i)/(b^4*d) - (a^2*atan(((a^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^6 - a^2*b^4) + (a^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^6 - a^2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b - A*B^2*a^2*b^9 + 2*A*B^2*a^3*b^8 - 9*A*B^2*a^4*b^7 + 12*A*B^2*a^5*b^6 - 16*A*B^2*a^6*b^5 + 12*A*B^2*a^7*b^4 + 4*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 14*A^2*B*a^5*b^6 - 12*A^2*B*a^6*b^5 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4 + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2 + 2*A*B*C*a^3*b^8 - 4*A*B*C*a^4*b^7 + 18*A*B*C*a^5*b^6 - 24*A*B*C*a^6*b^5 + 32*A*B*C*a^7*b^4 - 24*A*B*C*a^8*b^3))/b^9 - (a^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4) + (a^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(b^6 - a^2*b^4))","B"
901,1,5489,153,12.100493,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-2\,C\,a+C\,b\right)}{b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a-2\,B\,b+C\,b\right)}{b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^3}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^3}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(4\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7-12\,A^2\,B\,a^3\,b^5+12\,A^2\,B\,a^2\,b^6+12\,A^2\,C\,a^4\,b^4-14\,A^2\,C\,a^3\,b^5+6\,A^2\,C\,a^2\,b^6-4\,A^2\,C\,a\,b^7+12\,A\,B^2\,a^4\,b^4-12\,A\,B^2\,a^3\,b^5-24\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-12\,A\,B\,C\,a^3\,b^5+8\,A\,B\,C\,a^2\,b^6+12\,A\,C^2\,a^6\,b^2-16\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4-9\,A\,C^2\,a^3\,b^5+2\,A\,C^2\,a^2\,b^6-A\,C^2\,a\,b^7-4\,B^3\,a^5\,b^3+4\,B^3\,a^4\,b^4+12\,B^2\,C\,a^6\,b^2-14\,B^2\,C\,a^5\,b^3+6\,B^2\,C\,a^4\,b^4-4\,B^2\,C\,a^3\,b^5-12\,B\,C^2\,a^7\,b+16\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3+9\,B\,C^2\,a^4\,b^4-2\,B\,C^2\,a^3\,b^5+B\,C^2\,a^2\,b^6+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^3}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^3}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^3}}\right)\,\left(C\,a^2-B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^3\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}+\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}}{\frac{16\,\left(4\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7-12\,A^2\,B\,a^3\,b^5+12\,A^2\,B\,a^2\,b^6+12\,A^2\,C\,a^4\,b^4-14\,A^2\,C\,a^3\,b^5+6\,A^2\,C\,a^2\,b^6-4\,A^2\,C\,a\,b^7+12\,A\,B^2\,a^4\,b^4-12\,A\,B^2\,a^3\,b^5-24\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-12\,A\,B\,C\,a^3\,b^5+8\,A\,B\,C\,a^2\,b^6+12\,A\,C^2\,a^6\,b^2-16\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4-9\,A\,C^2\,a^3\,b^5+2\,A\,C^2\,a^2\,b^6-A\,C^2\,a\,b^7-4\,B^3\,a^5\,b^3+4\,B^3\,a^4\,b^4+12\,B^2\,C\,a^6\,b^2-14\,B^2\,C\,a^5\,b^3+6\,B^2\,C\,a^4\,b^4-4\,B^2\,C\,a^3\,b^5-12\,B\,C^2\,a^7\,b+16\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3+9\,B\,C^2\,a^4\,b^4-2\,B\,C^2\,a^3\,b^5+B\,C^2\,a^2\,b^6+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}-\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}+\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{a\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^5-a^2\,b^3\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*B*b - 2*C*a + C*b))/b^2 + (tan(c/2 + (d*x)/2)^3*(2*C*a - 2*B*b + C*b))/b^2)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2) - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2 + b^2*(A + C/2) - B*a*b))/b^3)*(C*a^2 + b^2*(A + C/2) - B*a*b)*1i)/b^3 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2) - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2 + b^2*(A + C/2) - B*a*b))/b^3)*(C*a^2 + b^2*(A + C/2) - B*a*b)*1i)/b^3)/((16*(4*C^3*a^8 - 4*A^3*a*b^7 - 6*C^3*a^7*b + 4*A^3*a^2*b^6 + 4*B^3*a^4*b^4 - 4*B^3*a^5*b^3 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - A*C^2*a*b^7 - 4*A^2*C*a*b^7 - 12*B*C^2*a^7*b - 12*A*B^2*a^3*b^5 + 12*A*B^2*a^4*b^4 + 12*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 2*A*C^2*a^2*b^6 - 9*A*C^2*a^3*b^5 + 12*A*C^2*a^4*b^4 - 16*A*C^2*a^5*b^3 + 12*A*C^2*a^6*b^2 + 6*A^2*C*a^2*b^6 - 14*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 + B*C^2*a^2*b^6 - 2*B*C^2*a^3*b^5 + 9*B*C^2*a^4*b^4 - 12*B*C^2*a^5*b^3 + 16*B*C^2*a^6*b^2 - 4*B^2*C*a^3*b^5 + 6*B^2*C*a^4*b^4 - 14*B^2*C*a^5*b^3 + 12*B^2*C*a^6*b^2 + 8*A*B*C*a^2*b^6 - 12*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 24*A*B*C*a^5*b^3))/b^6 - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2) - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2 + b^2*(A + C/2) - B*a*b))/b^3)*(C*a^2 + b^2*(A + C/2) - B*a*b))/b^3 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(C*a^2 + b^2*(A + C/2) - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2 + b^2*(A + C/2) - B*a*b))/b^3)*(C*a^2 + b^2*(A + C/2) - B*a*b))/b^3))*(C*a^2 + b^2*(A + C/2) - B*a*b)*2i)/(b^3*d) + (a*atan(((a*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (a*((a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*a*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^5 - a^2*b^3) + (a*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (a*((a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*a*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^5 - a^2*b^3))/((16*(4*C^3*a^8 - 4*A^3*a*b^7 - 6*C^3*a^7*b + 4*A^3*a^2*b^6 + 4*B^3*a^4*b^4 - 4*B^3*a^5*b^3 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - A*C^2*a*b^7 - 4*A^2*C*a*b^7 - 12*B*C^2*a^7*b - 12*A*B^2*a^3*b^5 + 12*A*B^2*a^4*b^4 + 12*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 2*A*C^2*a^2*b^6 - 9*A*C^2*a^3*b^5 + 12*A*C^2*a^4*b^4 - 16*A*C^2*a^5*b^3 + 12*A*C^2*a^6*b^2 + 6*A^2*C*a^2*b^6 - 14*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 + B*C^2*a^2*b^6 - 2*B*C^2*a^3*b^5 + 9*B*C^2*a^4*b^4 - 12*B*C^2*a^5*b^3 + 16*B*C^2*a^6*b^2 - 4*B^2*C*a^3*b^5 + 6*B^2*C*a^4*b^4 - 14*B^2*C*a^5*b^3 + 12*B^2*C*a^6*b^2 + 8*A*B*C*a^2*b^6 - 12*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 24*A*B*C*a^5*b^3))/b^6 - (a*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (a*((a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*a*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3) + (a*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (a*((a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*a*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(b^5 - a^2*b^3))","B"
902,1,3452,106,11.155751,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))),x)","-\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(B\,b-C\,a\right)\,\left(\frac{\left(B\,b-C\,a\right)\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^4}\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}\right)\,1{}\mathrm{i}}{b^2}-\frac{\left(B\,b-C\,a\right)\,\left(\frac{\left(B\,b-C\,a\right)\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^4}\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}\right)\,1{}\mathrm{i}}{b^2}}{\frac{64\,\left(-A^2\,B\,a\,b^4+A^2\,B\,b^5+A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,B^2\,a^2\,b^3-A\,B^2\,b^5-2\,A\,B\,C\,a^3\,b^2+2\,A\,B\,C\,a\,b^4+A\,C^2\,a^4\,b-A\,C^2\,a^2\,b^3-B^3\,a^2\,b^3+B^3\,a\,b^4+3\,B^2\,C\,a^3\,b^2-3\,B^2\,C\,a^2\,b^3-3\,B\,C^2\,a^4\,b+3\,B\,C^2\,a^3\,b^2+C^3\,a^5-C^3\,a^4\,b\right)}{b^3}+\frac{\left(B\,b-C\,a\right)\,\left(\frac{\left(B\,b-C\,a\right)\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^4}\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}\right)}{b^2}+\frac{\left(B\,b-C\,a\right)\,\left(\frac{\left(B\,b-C\,a\right)\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^4}\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}\right)}{b^2}}\right)\,\left(B\,b-C\,a\right)\,2{}\mathrm{i}}{b^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^2\,\left(b^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^4-a^2\,b^2}+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^2\,\left(b^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^4-a^2\,b^2}}{\frac{64\,\left(-A^2\,B\,a\,b^4+A^2\,B\,b^5+A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,B^2\,a^2\,b^3-A\,B^2\,b^5-2\,A\,B\,C\,a^3\,b^2+2\,A\,B\,C\,a\,b^4+A\,C^2\,a^4\,b-A\,C^2\,a^2\,b^3-B^3\,a^2\,b^3+B^3\,a\,b^4+3\,B^2\,C\,a^3\,b^2-3\,B^2\,C\,a^2\,b^3-3\,B\,C^2\,a^4\,b+3\,B\,C^2\,a^3\,b^2+C^3\,a^5-C^3\,a^4\,b\right)}{b^3}+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^2\,\left(b^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^4-a^2\,b^2}-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a\,b^4+A^2\,b^5+2\,A\,B\,a^2\,b^3-2\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-2\,B^2\,a^3\,b^2+4\,B^2\,a^2\,b^3-3\,B^2\,a\,b^4+B^2\,b^5+4\,B\,C\,a^4\,b-8\,B\,C\,a^3\,b^2+6\,B\,C\,a^2\,b^3-2\,B\,C\,a\,b^4-2\,C^2\,a^5+4\,C^2\,a^4\,b-3\,C^2\,a^3\,b^2+C^2\,a^2\,b^3\right)}{b^2}-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(A\,b^7+B\,b^7+A\,a^2\,b^5+B\,a^2\,b^5+2\,C\,a^2\,b^5-C\,a^3\,b^4-2\,A\,a\,b^6-2\,B\,a\,b^6-C\,a\,b^6\right)}{b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^3\,b^4-4\,a^2\,b^5+2\,a\,b^6\right)}{b^2\,\left(b^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^4-a^2\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^4-a^2\,b^2\right)}","Not used",1,"- (atan(-(((B*b - C*a)*(((B*b - C*a)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 - (32*tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/b^4))/b^2 - (32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2)*1i)/b^2 - ((B*b - C*a)*(((B*b - C*a)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 + (32*tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/b^4))/b^2 + (32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2)*1i)/b^2)/((64*(C^3*a^5 - A*B^2*b^5 + A^2*B*b^5 + B^3*a*b^4 - C^3*a^4*b - B^3*a^2*b^3 - A^2*B*a*b^4 + A*C^2*a^4*b - A^2*C*a*b^4 - 3*B*C^2*a^4*b + A*B^2*a^2*b^3 - A*C^2*a^2*b^3 + A^2*C*a^2*b^3 + 3*B*C^2*a^3*b^2 - 3*B^2*C*a^2*b^3 + 3*B^2*C*a^3*b^2 + 2*A*B*C*a*b^4 - 2*A*B*C*a^3*b^2))/b^3 + ((B*b - C*a)*(((B*b - C*a)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 - (32*tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/b^4))/b^2 - (32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2))/b^2 + ((B*b - C*a)*(((B*b - C*a)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 + (32*tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/b^4))/b^2 + (32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2))/b^2))*(B*b - C*a)*2i)/(b^2*d) - (atan(((((a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2 + (((a + b)*(a - b))^(1/2)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 + (32*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/(b^2*(b^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(b^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^4 - a^2*b^2) + (((a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2 - (((a + b)*(a - b))^(1/2)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 - (32*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/(b^2*(b^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(b^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^4 - a^2*b^2))/((64*(C^3*a^5 - A*B^2*b^5 + A^2*B*b^5 + B^3*a*b^4 - C^3*a^4*b - B^3*a^2*b^3 - A^2*B*a*b^4 + A*C^2*a^4*b - A^2*C*a*b^4 - 3*B*C^2*a^4*b + A*B^2*a^2*b^3 - A*C^2*a^2*b^3 + A^2*C*a^2*b^3 + 3*B*C^2*a^3*b^2 - 3*B^2*C*a^2*b^3 + 3*B^2*C*a^3*b^2 + 2*A*B*C*a*b^4 - 2*A*B*C*a^3*b^2))/b^3 + (((a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2 + (((a + b)*(a - b))^(1/2)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 + (32*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/(b^2*(b^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(b^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b))/(b^4 - a^2*b^2) - (((a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^5 + B^2*b^5 - 2*C^2*a^5 - A^2*a*b^4 - 3*B^2*a*b^4 + 4*C^2*a^4*b + 4*B^2*a^2*b^3 - 2*B^2*a^3*b^2 + C^2*a^2*b^3 - 3*C^2*a^3*b^2 - 2*A*B*a*b^4 - 2*B*C*a*b^4 + 4*B*C*a^4*b + 2*A*B*a^2*b^3 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 + 6*B*C*a^2*b^3 - 8*B*C*a^3*b^2))/b^2 - (((a + b)*(a - b))^(1/2)*((32*(A*b^7 + B*b^7 + A*a^2*b^5 + B*a^2*b^5 + 2*C*a^2*b^5 - C*a^3*b^4 - 2*A*a*b^6 - 2*B*a*b^6 - C*a*b^6))/b^3 - (32*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a*b^6 - 4*a^2*b^5 + 2*a^3*b^4))/(b^2*(b^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(b^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b))/(b^4 - a^2*b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(b^4 - a^2*b^2)) - (2*C*tan(c/2 + (d*x)/2))/(b*d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
903,1,18184,94,15.577489,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x)),x)","\frac{2\,C\,\mathrm{atanh}\left(\frac{16384\,C^5\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}+\frac{16384\,C^5\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,B^2\,C^3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,B\,C^4\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-16384\,A^4\,C\,a\,b^5+16384\,A^4\,C\,b^6+32768\,A^3\,B\,C\,a^2\,b^4-32768\,A^3\,B\,C\,a\,b^5-32768\,A^3\,C^2\,a^3\,b^3+32768\,A^3\,C^2\,a^2\,b^4-16384\,A^2\,B^2\,C\,a^3\,b^3+16384\,A^2\,B^2\,C\,a^2\,b^4+32768\,A^2\,B\,C^2\,a^4\,b^2-32768\,A^2\,B\,C^2\,a^3\,b^3-32768\,A^2\,C^3\,a^3\,b^3+32768\,A^2\,C^3\,a^2\,b^4+32768\,A\,B\,C^3\,a^4\,b^2-32768\,A\,B\,C^3\,a^3\,b^3-32768\,A\,C^4\,a^5\,b+32768\,A\,C^4\,a^4\,b^2-16384\,B^2\,C^3\,a^5\,b+16384\,B^2\,C^3\,a^4\,b^2+32768\,B\,C^4\,a^6-32768\,B\,C^4\,a^5\,b-16384\,C^5\,a^5\,b+16384\,C^5\,a^4\,b^2}+\frac{32768\,A\,C^4\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}+\frac{32768\,B\,C^4\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}+\frac{32768\,A\,C^4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,A^4\,C\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,B^2\,C^3\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}-\frac{16384\,A^4\,C\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A^2\,B\,C^2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{32768\,A^2\,C^3\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{32768\,A^3\,C^2\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A^2\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A^3\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A\,B\,C^3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,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,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A\,B\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{16384\,A\,B^2\,C^2\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{32768\,A^2\,B\,C^2\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,A\,B^2\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}\right)}{a\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A^3\,b^6-24576\,C^3\,a^6-8192\,A^2\,B\,b^6+8192\,B\,C^2\,a^6-49152\,A^3\,a\,b^5+49152\,C^3\,a^5\,b+32768\,A^3\,a^2\,b^4-8192\,A^3\,a^3\,b^3+8192\,C^3\,a^3\,b^3-32768\,C^3\,a^4\,b^2+8192\,A\,B^2\,a\,b^5-16384\,A^2\,B\,a\,b^5-8192\,A\,C^2\,a^5\,b+8192\,A^2\,C\,a\,b^5+16384\,B\,C^2\,a^5\,b-8192\,B^2\,C\,a^5\,b+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}-8192\,A\,B^2\,a^2\,b^4+49152\,A^2\,B\,a^2\,b^4-32768\,A^2\,B\,a^3\,b^3+8192\,A^2\,B\,a^4\,b^2-24576\,A\,C^2\,a^2\,b^4+65536\,A\,C^2\,a^3\,b^3-32768\,A\,C^2\,a^4\,b^2+32768\,A^2\,C\,a^2\,b^4-65536\,A^2\,C\,a^3\,b^3+24576\,A^2\,C\,a^4\,b^2-8192\,B\,C^2\,a^2\,b^4+32768\,B\,C^2\,a^3\,b^3-49152\,B\,C^2\,a^4\,b^2+8192\,B^2\,C\,a^4\,b^2-16384\,A\,B\,C\,a^2\,b^4+16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a\,b^3-a^3\,b}+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,C^3\,a^6-24576\,A^3\,b^6+8192\,A^2\,B\,b^6-8192\,B\,C^2\,a^6+49152\,A^3\,a\,b^5-49152\,C^3\,a^5\,b-32768\,A^3\,a^2\,b^4+8192\,A^3\,a^3\,b^3-8192\,C^3\,a^3\,b^3+32768\,C^3\,a^4\,b^2-8192\,A\,B^2\,a\,b^5+16384\,A^2\,B\,a\,b^5+8192\,A\,C^2\,a^5\,b-8192\,A^2\,C\,a\,b^5-16384\,B\,C^2\,a^5\,b+8192\,B^2\,C\,a^5\,b+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+8192\,A\,B^2\,a^2\,b^4-49152\,A^2\,B\,a^2\,b^4+32768\,A^2\,B\,a^3\,b^3-8192\,A^2\,B\,a^4\,b^2+24576\,A\,C^2\,a^2\,b^4-65536\,A\,C^2\,a^3\,b^3+32768\,A\,C^2\,a^4\,b^2-32768\,A^2\,C\,a^2\,b^4+65536\,A^2\,C\,a^3\,b^3-24576\,A^2\,C\,a^4\,b^2+8192\,B\,C^2\,a^2\,b^4-32768\,B\,C^2\,a^3\,b^3+49152\,B\,C^2\,a^4\,b^2-8192\,B^2\,C\,a^4\,b^2+16384\,A\,B\,C\,a^2\,b^4-16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a\,b^3-a^3\,b}}{49152\,A^2\,C^3\,a^4-16384\,A^4\,C\,b^4-16384\,A\,C^4\,a^4+49152\,A^3\,C^2\,b^4+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A^3\,b^6-24576\,C^3\,a^6-8192\,A^2\,B\,b^6+8192\,B\,C^2\,a^6-49152\,A^3\,a\,b^5+49152\,C^3\,a^5\,b+32768\,A^3\,a^2\,b^4-8192\,A^3\,a^3\,b^3+8192\,C^3\,a^3\,b^3-32768\,C^3\,a^4\,b^2+8192\,A\,B^2\,a\,b^5-16384\,A^2\,B\,a\,b^5-8192\,A\,C^2\,a^5\,b+8192\,A^2\,C\,a\,b^5+16384\,B\,C^2\,a^5\,b-8192\,B^2\,C\,a^5\,b+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}-8192\,A\,B^2\,a^2\,b^4+49152\,A^2\,B\,a^2\,b^4-32768\,A^2\,B\,a^3\,b^3+8192\,A^2\,B\,a^4\,b^2-24576\,A\,C^2\,a^2\,b^4+65536\,A\,C^2\,a^3\,b^3-32768\,A\,C^2\,a^4\,b^2+32768\,A^2\,C\,a^2\,b^4-65536\,A^2\,C\,a^3\,b^3+24576\,A^2\,C\,a^4\,b^2-8192\,B\,C^2\,a^2\,b^4+32768\,B\,C^2\,a^3\,b^3-49152\,B\,C^2\,a^4\,b^2+8192\,B^2\,C\,a^4\,b^2-16384\,A\,B\,C\,a^2\,b^4+16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,C^3\,a^6-24576\,A^3\,b^6+8192\,A^2\,B\,b^6-8192\,B\,C^2\,a^6+49152\,A^3\,a\,b^5-49152\,C^3\,a^5\,b-32768\,A^3\,a^2\,b^4+8192\,A^3\,a^3\,b^3-8192\,C^3\,a^3\,b^3+32768\,C^3\,a^4\,b^2-8192\,A\,B^2\,a\,b^5+16384\,A^2\,B\,a\,b^5+8192\,A\,C^2\,a^5\,b-8192\,A^2\,C\,a\,b^5-16384\,B\,C^2\,a^5\,b+8192\,B^2\,C\,a^5\,b+\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)-\frac{\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+8192\,A\,B^2\,a^2\,b^4-49152\,A^2\,B\,a^2\,b^4+32768\,A^2\,B\,a^3\,b^3-8192\,A^2\,B\,a^4\,b^2+24576\,A\,C^2\,a^2\,b^4-65536\,A\,C^2\,a^3\,b^3+32768\,A\,C^2\,a^4\,b^2-32768\,A^2\,C\,a^2\,b^4+65536\,A^2\,C\,a^3\,b^3-24576\,A^2\,C\,a^4\,b^2+8192\,B\,C^2\,a^2\,b^4-32768\,B\,C^2\,a^3\,b^3+49152\,B\,C^2\,a^4\,b^2-8192\,B^2\,C\,a^4\,b^2+16384\,A\,B\,C\,a^2\,b^4-16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+16384\,A\,C^4\,a^3\,b+16384\,A^4\,C\,a\,b^3-16384\,A^2\,B\,C^2\,a^4-16384\,A^2\,B\,C^2\,b^4+16384\,A^2\,C^3\,a\,b^3-98304\,A^2\,C^3\,a^3\,b-98304\,A^3\,C^2\,a\,b^3+16384\,A^3\,C^2\,a^3\,b-32768\,A\,B\,C^3\,a^2\,b^2+16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a^3\,b+16384\,A^2\,B^2\,C\,a^3\,b-32768\,A^3\,B\,C\,a^2\,b^2-16384\,A\,B^2\,C^2\,a^2\,b^2+98304\,A^2\,B\,C^2\,a^2\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^2+32768\,A\,B\,C^3\,a^3\,b+32768\,A^3\,B\,C\,a\,b^3}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a\,b^3-a^3\,b\right)}","Not used",1,"(2*C*atanh((16384*C^5*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) + (16384*C^5*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*B^2*C^3*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*B*C^4*a^6*tan(c/2 + (d*x)/2))/(32768*B*C^4*a^6 + 16384*A^4*C*b^6 - 16384*C^5*a^5*b + 16384*C^5*a^4*b^2 + 32768*A^2*C^3*a^2*b^4 - 32768*A^2*C^3*a^3*b^3 + 32768*A^3*C^2*a^2*b^4 - 32768*A^3*C^2*a^3*b^3 + 16384*B^2*C^3*a^4*b^2 - 32768*A*C^4*a^5*b - 16384*A^4*C*a*b^5 - 32768*B*C^4*a^5*b + 32768*A*C^4*a^4*b^2 - 16384*B^2*C^3*a^5*b - 32768*A*B*C^3*a^3*b^3 + 32768*A*B*C^3*a^4*b^2 + 32768*A^3*B*C*a^2*b^4 - 32768*A^2*B*C^2*a^3*b^3 + 32768*A^2*B*C^2*a^4*b^2 + 16384*A^2*B^2*C*a^2*b^4 - 16384*A^2*B^2*C*a^3*b^3 - 32768*A^3*B*C*a*b^5) + (32768*A*C^4*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) + (32768*B*C^4*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) + (32768*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*B^2*C^3*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) - (16384*A^4*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^2*B*C^2*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*C^2*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A*B*C^3*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A^2*B^2*C*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A*B*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*B*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*B*C^2*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (16384*A^2*B^2*C*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*B*C*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3)))/(b*d) + (2*A*atan((16384*A^5*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (16384*A^5*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^4*B*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (32768*A^4*C*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (16384*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A^3*B^2*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (16384*A^3*B^2*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^4*B*b^6*tan(c/2 + (d*x)/2))/(16384*A*C^4*a^6 + 32768*A^4*B*b^6 - 16384*A^5*a*b^5 + 16384*A^5*a^2*b^4 + 16384*A^3*B^2*a^2*b^4 - 32768*A^2*C^3*a^3*b^3 + 32768*A^2*C^3*a^4*b^2 - 32768*A^3*C^2*a^3*b^3 + 32768*A^3*C^2*a^4*b^2 - 32768*A^4*B*a*b^5 - 16384*A*C^4*a^5*b - 32768*A^4*C*a*b^5 - 16384*A^3*B^2*a*b^5 + 32768*A^4*C*a^2*b^4 + 32768*A*B*C^3*a^4*b^2 + 32768*A^3*B*C*a^2*b^4 - 32768*A^3*B*C*a^3*b^3 - 16384*A*B^2*C^2*a^3*b^3 + 16384*A*B^2*C^2*a^4*b^2 + 32768*A^2*B*C^2*a^2*b^4 - 32768*A^2*B*C^2*a^3*b^3 - 32768*A*B*C^3*a^5*b) + (32768*A^2*B*C^2*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*C^3*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*B*C*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (16384*A*C^4*a^3*b*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A*B*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*B*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A*B*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (16384*A*B^2*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*B*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A*B^2*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3)))/(a*d) + (atan(((((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A^3*b^6 - 24576*C^3*a^6 - 8192*A^2*B*b^6 + 8192*B*C^2*a^6 - 49152*A^3*a*b^5 + 49152*C^3*a^5*b + 32768*A^3*a^2*b^4 - 8192*A^3*a^3*b^3 + 8192*C^3*a^3*b^3 - 32768*C^3*a^4*b^2 + 8192*A*B^2*a*b^5 - 16384*A^2*B*a*b^5 - 8192*A*C^2*a^5*b + 8192*A^2*C*a*b^5 + 16384*B*C^2*a^5*b - 8192*B^2*C*a^5*b + (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) + (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 + (tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) - 8192*A*B^2*a^2*b^4 + 49152*A^2*B*a^2*b^4 - 32768*A^2*B*a^3*b^3 + 8192*A^2*B*a^4*b^2 - 24576*A*C^2*a^2*b^4 + 65536*A*C^2*a^3*b^3 - 32768*A*C^2*a^4*b^2 + 32768*A^2*C*a^2*b^4 - 65536*A^2*C*a^3*b^3 + 24576*A^2*C*a^4*b^2 - 8192*B*C^2*a^2*b^4 + 32768*B*C^2*a^3*b^3 - 49152*B*C^2*a^4*b^2 + 8192*B^2*C*a^4*b^2 - 16384*A*B*C*a^2*b^4 + 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a*b^3 - a^3*b) + (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*C^3*a^6 - 24576*A^3*b^6 + 8192*A^2*B*b^6 - 8192*B*C^2*a^6 + 49152*A^3*a*b^5 - 49152*C^3*a^5*b - 32768*A^3*a^2*b^4 + 8192*A^3*a^3*b^3 - 8192*C^3*a^3*b^3 + 32768*C^3*a^4*b^2 - 8192*A*B^2*a*b^5 + 16384*A^2*B*a*b^5 + 8192*A*C^2*a^5*b - 8192*A^2*C*a*b^5 - 16384*B*C^2*a^5*b + 8192*B^2*C*a^5*b + (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 - (tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + 8192*A*B^2*a^2*b^4 - 49152*A^2*B*a^2*b^4 + 32768*A^2*B*a^3*b^3 - 8192*A^2*B*a^4*b^2 + 24576*A*C^2*a^2*b^4 - 65536*A*C^2*a^3*b^3 + 32768*A*C^2*a^4*b^2 - 32768*A^2*C*a^2*b^4 + 65536*A^2*C*a^3*b^3 - 24576*A^2*C*a^4*b^2 + 8192*B*C^2*a^2*b^4 - 32768*B*C^2*a^3*b^3 + 49152*B*C^2*a^4*b^2 - 8192*B^2*C*a^4*b^2 + 16384*A*B*C*a^2*b^4 - 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a*b^3 - a^3*b))/(49152*A^2*C^3*a^4 - 16384*A^4*C*b^4 - 16384*A*C^4*a^4 + 49152*A^3*C^2*b^4 + (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A^3*b^6 - 24576*C^3*a^6 - 8192*A^2*B*b^6 + 8192*B*C^2*a^6 - 49152*A^3*a*b^5 + 49152*C^3*a^5*b + 32768*A^3*a^2*b^4 - 8192*A^3*a^3*b^3 + 8192*C^3*a^3*b^3 - 32768*C^3*a^4*b^2 + 8192*A*B^2*a*b^5 - 16384*A^2*B*a*b^5 - 8192*A*C^2*a^5*b + 8192*A^2*C*a*b^5 + 16384*B*C^2*a^5*b - 8192*B^2*C*a^5*b + (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) + (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 + (tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) - 8192*A*B^2*a^2*b^4 + 49152*A^2*B*a^2*b^4 - 32768*A^2*B*a^3*b^3 + 8192*A^2*B*a^4*b^2 - 24576*A*C^2*a^2*b^4 + 65536*A*C^2*a^3*b^3 - 32768*A*C^2*a^4*b^2 + 32768*A^2*C*a^2*b^4 - 65536*A^2*C*a^3*b^3 + 24576*A^2*C*a^4*b^2 - 8192*B*C^2*a^2*b^4 + 32768*B*C^2*a^3*b^3 - 49152*B*C^2*a^4*b^2 + 8192*B^2*C*a^4*b^2 - 16384*A*B*C*a^2*b^4 + 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) - (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*C^3*a^6 - 24576*A^3*b^6 + 8192*A^2*B*b^6 - 8192*B*C^2*a^6 + 49152*A^3*a*b^5 - 49152*C^3*a^5*b - 32768*A^3*a^2*b^4 + 8192*A^3*a^3*b^3 - 8192*C^3*a^3*b^3 + 32768*C^3*a^4*b^2 - 8192*A*B^2*a*b^5 + 16384*A^2*B*a*b^5 + 8192*A*C^2*a^5*b - 8192*A^2*C*a*b^5 - 16384*B*C^2*a^5*b + 8192*B^2*C*a^5*b + (((a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) - (((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 - (tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + 8192*A*B^2*a^2*b^4 - 49152*A^2*B*a^2*b^4 + 32768*A^2*B*a^3*b^3 - 8192*A^2*B*a^4*b^2 + 24576*A*C^2*a^2*b^4 - 65536*A*C^2*a^3*b^3 + 32768*A*C^2*a^4*b^2 - 32768*A^2*C*a^2*b^4 + 65536*A^2*C*a^3*b^3 - 24576*A^2*C*a^4*b^2 + 8192*B*C^2*a^2*b^4 - 32768*B*C^2*a^3*b^3 + 49152*B*C^2*a^4*b^2 - 8192*B^2*C*a^4*b^2 + 16384*A*B*C*a^2*b^4 - 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 16384*A*C^4*a^3*b + 16384*A^4*C*a*b^3 - 16384*A^2*B*C^2*a^4 - 16384*A^2*B*C^2*b^4 + 16384*A^2*C^3*a*b^3 - 98304*A^2*C^3*a^3*b - 98304*A^3*C^2*a*b^3 + 16384*A^3*C^2*a^3*b - 32768*A*B*C^3*a^2*b^2 + 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 - 32768*A^2*B*C^2*a^3*b + 16384*A^2*B^2*C*a^3*b - 32768*A^3*B*C*a^2*b^2 - 16384*A*B^2*C^2*a^2*b^2 + 98304*A^2*B*C^2*a^2*b^2 - 16384*A^2*B^2*C*a^2*b^2 + 32768*A*B*C^3*a^3*b + 32768*A^3*B*C*a*b^3))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a*b^3 - a^3*b))","B"
904,1,4410,98,8.376485,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{2\,A\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{2\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{A\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{A\,b^2\,\mathrm{atan}\left(\frac{A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+B^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}-C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+B^2\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A\,B\,a\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}-A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}+A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,B\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,6{}\mathrm{i}-A\,B\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,B\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}+A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B\,C\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}-B\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+B\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^7\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^5\,b^3-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b^5+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+B^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}-C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+B^2\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A\,B\,a\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}-A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}+A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,B\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,6{}\mathrm{i}-A\,B\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,B\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}+A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B\,C\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}-B\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+B\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^7\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^5\,b^3-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b^5+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}-\frac{2\,A\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{2\,B\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{B\,a\,b\,\mathrm{atan}\left(\frac{A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+B^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}-C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+B^2\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}-A\,B\,a\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}-A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,4{}\mathrm{i}+A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,B\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,6{}\mathrm{i}-A\,B\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,B\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}+A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B\,C\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,4{}\mathrm{i}-B\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-B\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}+B\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^7\,b+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^5\,b^3-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b^5+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}","Not used",1,"(2*A*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) + (2*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) + (A*a^3*sin(c + d*x))/(d*(a^4 - a^2*b^2)) - (A*a*b^2*sin(c + d*x))/(d*(a^4 - a^2*b^2)) + (A*b^2*atan((A^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + B^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - C^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + B^2*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A*B*a*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i - A*B*a*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*4i + A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*B*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*6i - A*B*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*B*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i + A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B*C*a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i - B*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + B*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i)/(B^2*a^8*cos(c/2 + (d*x)/2) + C^2*a^8*cos(c/2 + (d*x)/2) + A^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*A^2*a^4*b^4*cos(c/2 + (d*x)/2) + A^2*a^6*b^2*cos(c/2 + (d*x)/2) + B^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*B^2*a^6*b^2*cos(c/2 + (d*x)/2) + C^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*C^2*a^6*b^2*cos(c/2 + (d*x)/2) - 2*A*B*a^3*b^5*cos(c/2 + (d*x)/2) + 4*A*B*a^5*b^3*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2) - 2*B*C*a^3*b^5*cos(c/2 + (d*x)/2) + 4*B*C*a^5*b^3*cos(c/2 + (d*x)/2) - 2*A*B*a^7*b*cos(c/2 + (d*x)/2) - 2*B*C*a^7*b*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2)) + (C*a^2*atan((A^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + B^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - C^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + B^2*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A*B*a*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i - A*B*a*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*4i + A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*B*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*6i - A*B*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*B*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i + A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B*C*a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i - B*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + B*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i)/(B^2*a^8*cos(c/2 + (d*x)/2) + C^2*a^8*cos(c/2 + (d*x)/2) + A^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*A^2*a^4*b^4*cos(c/2 + (d*x)/2) + A^2*a^6*b^2*cos(c/2 + (d*x)/2) + B^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*B^2*a^6*b^2*cos(c/2 + (d*x)/2) + C^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*C^2*a^6*b^2*cos(c/2 + (d*x)/2) - 2*A*B*a^3*b^5*cos(c/2 + (d*x)/2) + 4*A*B*a^5*b^3*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2) - 2*B*C*a^3*b^5*cos(c/2 + (d*x)/2) + 4*B*C*a^5*b^3*cos(c/2 + (d*x)/2) - 2*A*B*a^7*b*cos(c/2 + (d*x)/2) - 2*B*C*a^7*b*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2)) - (2*A*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) - (2*B*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) - (B*a*b*atan((A^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + A^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - C^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + B^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - C^2*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + B^2*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i + B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i - A*B*a*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i - A*B*a*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*4i + A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + B*C*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*B*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*6i - A*B*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*B*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i + A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B*C*a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*4i - B*C*a^3*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - B*C*a^4*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i + B*C*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i)/(B^2*a^8*cos(c/2 + (d*x)/2) + C^2*a^8*cos(c/2 + (d*x)/2) + A^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*A^2*a^4*b^4*cos(c/2 + (d*x)/2) + A^2*a^6*b^2*cos(c/2 + (d*x)/2) + B^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*B^2*a^6*b^2*cos(c/2 + (d*x)/2) + C^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*C^2*a^6*b^2*cos(c/2 + (d*x)/2) - 2*A*B*a^3*b^5*cos(c/2 + (d*x)/2) + 4*A*B*a^5*b^3*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2) - 2*B*C*a^3*b^5*cos(c/2 + (d*x)/2) + 4*B*C*a^5*b^3*cos(c/2 + (d*x)/2) - 2*A*B*a^7*b*cos(c/2 + (d*x)/2) - 2*B*C*a^7*b*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2))","B"
905,1,5581,145,12.197479,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a-2\,A\,b+2\,B\,a\right)}{a^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a+2\,A\,b-2\,B\,a\right)}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^3}}{\frac{16\,\left(-A^3\,a^5\,b^3+2\,A^3\,a^4\,b^4-5\,A^3\,a^3\,b^5+6\,A^3\,a^2\,b^6-6\,A^3\,a\,b^7+4\,A^3\,b^8+A^2\,B\,a^6\,b^2-2\,A^2\,B\,a^5\,b^3+9\,A^2\,B\,a^4\,b^4-12\,A^2\,B\,a^3\,b^5+16\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7-A^2\,C\,a^7\,b+2\,A^2\,C\,a^6\,b^2-9\,A^2\,C\,a^5\,b^3+12\,A^2\,C\,a^4\,b^4-16\,A^2\,C\,a^3\,b^5+12\,A^2\,C\,a^2\,b^6-4\,A\,B^2\,a^5\,b^3+6\,A\,B^2\,a^4\,b^4-14\,A\,B^2\,a^3\,b^5+12\,A\,B^2\,a^2\,b^6+8\,A\,B\,C\,a^6\,b^2-12\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-24\,A\,B\,C\,a^3\,b^5-4\,A\,C^2\,a^7\,b+6\,A\,C^2\,a^6\,b^2-14\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4+4\,B^3\,a^4\,b^4-4\,B^3\,a^3\,b^5-12\,B^2\,C\,a^5\,b^3+12\,B^2\,C\,a^4\,b^4+12\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3-4\,C^3\,a^7\,b+4\,C^3\,a^6\,b^2\right)}{a^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^3}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)}{a^3}}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-1{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,A\,b^2\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}}{\frac{16\,\left(-A^3\,a^5\,b^3+2\,A^3\,a^4\,b^4-5\,A^3\,a^3\,b^5+6\,A^3\,a^2\,b^6-6\,A^3\,a\,b^7+4\,A^3\,b^8+A^2\,B\,a^6\,b^2-2\,A^2\,B\,a^5\,b^3+9\,A^2\,B\,a^4\,b^4-12\,A^2\,B\,a^3\,b^5+16\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7-A^2\,C\,a^7\,b+2\,A^2\,C\,a^6\,b^2-9\,A^2\,C\,a^5\,b^3+12\,A^2\,C\,a^4\,b^4-16\,A^2\,C\,a^3\,b^5+12\,A^2\,C\,a^2\,b^6-4\,A\,B^2\,a^5\,b^3+6\,A\,B^2\,a^4\,b^4-14\,A\,B^2\,a^3\,b^5+12\,A\,B^2\,a^2\,b^6+8\,A\,B\,C\,a^6\,b^2-12\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-24\,A\,B\,C\,a^3\,b^5-4\,A\,C^2\,a^7\,b+6\,A\,C^2\,a^6\,b^2-14\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4+4\,B^3\,a^4\,b^4-4\,B^3\,a^3\,b^5-12\,B^2\,C\,a^5\,b^3+12\,B^2\,C\,a^4\,b^4+12\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3-4\,C^3\,a^7\,b+4\,C^3\,a^6\,b^2\right)}{a^6}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^5-a^3\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*a - 2*A*b + 2*B*a))/a^2 - (tan(c/2 + (d*x)/2)^3*(A*a + 2*A*b - 2*B*a))/a^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*tan(c/2 + (d*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^7)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^3)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i)*1i)/a^3 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*tan(c/2 + (d*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^7)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^3)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i)*1i)/a^3)/((16*(4*A^3*b^8 - 6*A^3*a*b^7 - 4*C^3*a^7*b + 6*A^3*a^2*b^6 - 5*A^3*a^3*b^5 + 2*A^3*a^4*b^4 - A^3*a^5*b^3 - 4*B^3*a^3*b^5 + 4*B^3*a^4*b^4 + 4*C^3*a^6*b^2 - 12*A^2*B*a*b^7 - 4*A*C^2*a^7*b - A^2*C*a^7*b + 12*A*B^2*a^2*b^6 - 14*A*B^2*a^3*b^5 + 6*A*B^2*a^4*b^4 - 4*A*B^2*a^5*b^3 + 16*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 9*A^2*B*a^4*b^4 - 2*A^2*B*a^5*b^3 + A^2*B*a^6*b^2 + 12*A*C^2*a^4*b^4 - 14*A*C^2*a^5*b^3 + 6*A*C^2*a^6*b^2 + 12*A^2*C*a^2*b^6 - 16*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 - 9*A^2*C*a^5*b^3 + 2*A^2*C*a^6*b^2 - 12*B*C^2*a^5*b^3 + 12*B*C^2*a^6*b^2 + 12*B^2*C*a^4*b^4 - 12*B^2*C*a^5*b^3 - 24*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 12*A*B*C*a^5*b^3 + 8*A*B*C*a^6*b^2))/a^6 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*tan(c/2 + (d*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^7)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^3)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^3 - (((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*tan(c/2 + (d*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^7)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^3)*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i))/a^3))*(A*b^2*1i + a^2*((A*1i)/2 + C*1i) - B*a*b*1i)*2i)/(a^3*d) - (b*atan(((b*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (b*((a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^5 - a^3*b^2) + (b*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (b*((a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^5 - a^3*b^2))/((16*(4*A^3*b^8 - 6*A^3*a*b^7 - 4*C^3*a^7*b + 6*A^3*a^2*b^6 - 5*A^3*a^3*b^5 + 2*A^3*a^4*b^4 - A^3*a^5*b^3 - 4*B^3*a^3*b^5 + 4*B^3*a^4*b^4 + 4*C^3*a^6*b^2 - 12*A^2*B*a*b^7 - 4*A*C^2*a^7*b - A^2*C*a^7*b + 12*A*B^2*a^2*b^6 - 14*A*B^2*a^3*b^5 + 6*A*B^2*a^4*b^4 - 4*A*B^2*a^5*b^3 + 16*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 9*A^2*B*a^4*b^4 - 2*A^2*B*a^5*b^3 + A^2*B*a^6*b^2 + 12*A*C^2*a^4*b^4 - 14*A*C^2*a^5*b^3 + 6*A*C^2*a^6*b^2 + 12*A^2*C*a^2*b^6 - 16*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 - 9*A^2*C*a^5*b^3 + 2*A^2*C*a^6*b^2 - 12*B*C^2*a^5*b^3 + 12*B*C^2*a^6*b^2 + 12*B^2*C*a^4*b^4 - 12*B^2*C*a^5*b^3 - 24*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 12*A*B*C*a^5*b^3 + 8*A*B*C*a^6*b^2))/a^6 + (b*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (b*((a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2) - (b*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (b*((a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^5 - a^3*b^2))","B"
906,1,7110,205,13.191438,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^2+3\,A\,b^2+3\,C\,a^2-3\,B\,a\,b\right)}{3\,a^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^2+2\,A\,b^2+B\,a^2+2\,C\,a^2-A\,a\,b-2\,B\,a\,b\right)}{a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^2+2\,A\,b^2-B\,a^2+2\,C\,a^2+A\,a\,b-2\,B\,a\,b\right)}{a^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}+3\,A^2\,B\,a^6\,b^5-6\,A^2\,B\,a^5\,b^6+15\,A^2\,B\,a^4\,b^7-18\,A^2\,B\,a^3\,b^8+18\,A^2\,B\,a^2\,b^9-12\,A^2\,B\,a\,b^{10}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-3\,A\,B^2\,a^7\,b^4+6\,A\,B^2\,a^6\,b^5-15\,A\,B^2\,a^5\,b^6+18\,A\,B^2\,a^4\,b^7-18\,A\,B^2\,a^3\,b^8+12\,A\,B^2\,a^2\,b^9+2\,A\,B\,C\,a^8\,b^3-4\,A\,B\,C\,a^7\,b^4+18\,A\,B\,C\,a^6\,b^5-24\,A\,B\,C\,a^5\,b^6+32\,A\,B\,C\,a^4\,b^7-24\,A\,B\,C\,a^3\,b^8-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7+B^3\,a^8\,b^3-2\,B^3\,a^7\,b^4+5\,B^3\,a^6\,b^5-6\,B^3\,a^5\,b^6+6\,B^3\,a^4\,b^7-4\,B^3\,a^3\,b^8-B^2\,C\,a^9\,b^2+2\,B^2\,C\,a^8\,b^3-9\,B^2\,C\,a^7\,b^4+12\,B^2\,C\,a^6\,b^5-16\,B^2\,C\,a^5\,b^6+12\,B^2\,C\,a^4\,b^7+4\,B\,C^2\,a^8\,b^3-6\,B\,C^2\,a^7\,b^4+14\,B\,C^2\,a^6\,b^5-12\,B\,C^2\,a^5\,b^6-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^4}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^{10}}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^4}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)}{a^4}}\right)\,\left(A\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(\frac{A\,b\,1{}\mathrm{i}}{2}+C\,b\,1{}\mathrm{i}\right)-B\,a\,b^2\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}+3\,A^2\,B\,a^6\,b^5-6\,A^2\,B\,a^5\,b^6+15\,A^2\,B\,a^4\,b^7-18\,A^2\,B\,a^3\,b^8+18\,A^2\,B\,a^2\,b^9-12\,A^2\,B\,a\,b^{10}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-3\,A\,B^2\,a^7\,b^4+6\,A\,B^2\,a^6\,b^5-15\,A\,B^2\,a^5\,b^6+18\,A\,B^2\,a^4\,b^7-18\,A\,B^2\,a^3\,b^8+12\,A\,B^2\,a^2\,b^9+2\,A\,B\,C\,a^8\,b^3-4\,A\,B\,C\,a^7\,b^4+18\,A\,B\,C\,a^6\,b^5-24\,A\,B\,C\,a^5\,b^6+32\,A\,B\,C\,a^4\,b^7-24\,A\,B\,C\,a^3\,b^8-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7+B^3\,a^8\,b^3-2\,B^3\,a^7\,b^4+5\,B^3\,a^6\,b^5-6\,B^3\,a^5\,b^6+6\,B^3\,a^4\,b^7-4\,B^3\,a^3\,b^8-B^2\,C\,a^9\,b^2+2\,B^2\,C\,a^8\,b^3-9\,B^2\,C\,a^7\,b^4+12\,B^2\,C\,a^6\,b^5-16\,B^2\,C\,a^5\,b^6+12\,B^2\,C\,a^4\,b^7+4\,B\,C^2\,a^8\,b^3-6\,B\,C^2\,a^7\,b^4+14\,B\,C^2\,a^6\,b^5-12\,B\,C^2\,a^5\,b^6-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"((4*tan(c/2 + (d*x)/2)^3*(A*a^2 + 3*A*b^2 + 3*C*a^2 - 3*B*a*b))/(3*a^3) + (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 + 2*C*a^2 - A*a*b - 2*B*a*b))/a^3 + (tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 2*A*b^2 - B*a^2 + 2*C*a^2 + A*a*b - 2*B*a*b))/a^3)/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) + (atan(-((((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^10)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^4)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i)*1i)/a^4 + (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^10)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^4)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i)*1i)/a^4)/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 - 4*B^3*a^3*b^8 + 6*B^3*a^4*b^7 - 6*B^3*a^5*b^6 + 5*B^3*a^6*b^5 - 2*B^3*a^7*b^4 + B^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*A^2*B*a*b^10 + 12*A*B^2*a^2*b^9 - 18*A*B^2*a^3*b^8 + 18*A*B^2*a^4*b^7 - 15*A*B^2*a^5*b^6 + 6*A*B^2*a^6*b^5 - 3*A*B^2*a^7*b^4 + 18*A^2*B*a^2*b^9 - 18*A^2*B*a^3*b^8 + 15*A^2*B*a^4*b^7 - 6*A^2*B*a^5*b^6 + 3*A^2*B*a^6*b^5 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4 - 12*B*C^2*a^5*b^6 + 14*B*C^2*a^6*b^5 - 6*B*C^2*a^7*b^4 + 4*B*C^2*a^8*b^3 + 12*B^2*C*a^4*b^7 - 16*B^2*C*a^5*b^6 + 12*B^2*C*a^6*b^5 - 9*B^2*C*a^7*b^4 + 2*B^2*C*a^8*b^3 - B^2*C*a^9*b^2 - 24*A*B*C*a^3*b^8 + 32*A*B*C*a^4*b^7 - 24*A*B*C*a^5*b^6 + 18*A*B*C*a^6*b^5 - 4*A*B*C*a^7*b^4 + 2*A*B*C*a^8*b^3))/a^9 + (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^10)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^4)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^4 - (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^10)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^4)*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i))/a^4))*(A*b^3*1i - (B*a^3*1i)/2 + a^2*((A*b*1i)/2 + C*b*1i) - B*a*b^2*1i)*2i)/(a^4*d) - (b^2*atan(((b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (b^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^6 - a^4*b^2) + (b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (b^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^6 - a^4*b^2))/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 - 4*B^3*a^3*b^8 + 6*B^3*a^4*b^7 - 6*B^3*a^5*b^6 + 5*B^3*a^6*b^5 - 2*B^3*a^7*b^4 + B^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*A^2*B*a*b^10 + 12*A*B^2*a^2*b^9 - 18*A*B^2*a^3*b^8 + 18*A*B^2*a^4*b^7 - 15*A*B^2*a^5*b^6 + 6*A*B^2*a^6*b^5 - 3*A*B^2*a^7*b^4 + 18*A^2*B*a^2*b^9 - 18*A^2*B*a^3*b^8 + 15*A^2*B*a^4*b^7 - 6*A^2*B*a^5*b^6 + 3*A^2*B*a^6*b^5 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4 - 12*B*C^2*a^5*b^6 + 14*B*C^2*a^6*b^5 - 6*B*C^2*a^7*b^4 + 4*B*C^2*a^8*b^3 + 12*B^2*C*a^4*b^7 - 16*B^2*C*a^5*b^6 + 12*B^2*C*a^6*b^5 - 9*B^2*C*a^7*b^4 + 2*B^2*C*a^8*b^3 - B^2*C*a^9*b^2 - 24*A*B*C*a^3*b^8 + 32*A*B*C*a^4*b^7 - 24*A*B*C*a^5*b^6 + 18*A*B*C*a^6*b^5 - 4*A*B*C*a^7*b^4 + 2*A*B*C*a^8*b^3))/a^9 + (b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (b^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2) - (b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (b^2*((a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^6 - a^4*b^2))","B"
907,1,9648,276,15.015673,"\text{Not used}","int((cos(c + d*x)^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,A\,a^3+8\,A\,b^3-8\,B\,a^3+4\,C\,a^3+4\,A\,a\,b^2+8\,A\,a^2\,b-8\,B\,a\,b^2-4\,B\,a^2\,b+8\,C\,a^2\,b\right)}{4\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,A\,a^3+72\,A\,b^3-40\,B\,a^3-12\,C\,a^3-12\,A\,a\,b^2+40\,A\,a^2\,b-72\,B\,a\,b^2+12\,B\,a^2\,b+72\,C\,a^2\,b\right)}{12\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,A\,b^3-9\,A\,a^3-40\,B\,a^3+12\,C\,a^3+12\,A\,a\,b^2+40\,A\,a^2\,b-72\,B\,a\,b^2-12\,B\,a^2\,b+72\,C\,a^2\,b\right)}{12\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^3-8\,A\,b^3+8\,B\,a^3+4\,C\,a^3+4\,A\,a\,b^2-8\,A\,a^2\,b+8\,B\,a\,b^2-4\,B\,a^2\,b-8\,C\,a^2\,b\right)}{4\,a^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{a^5}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{a^5}}{\frac{-9\,A^3\,a^9\,b^5+18\,A^3\,a^8\,b^6-33\,A^3\,a^7\,b^7+48\,A^3\,a^6\,b^8-88\,A^3\,a^5\,b^9+104\,A^3\,a^4\,b^{10}-104\,A^3\,a^3\,b^{11}+96\,A^3\,a^2\,b^{12}-96\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+9\,A^2\,B\,a^{10}\,b^4-18\,A^2\,B\,a^9\,b^5+57\,A^2\,B\,a^8\,b^6-96\,A^2\,B\,a^7\,b^7+192\,A^2\,B\,a^6\,b^8-240\,A^2\,B\,a^5\,b^9+288\,A^2\,B\,a^4\,b^{10}-288\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-192\,A^2\,B\,a\,b^{13}-9\,A^2\,C\,a^{11}\,b^3+18\,A^2\,C\,a^{10}\,b^4-57\,A^2\,C\,a^9\,b^5+96\,A^2\,C\,a^8\,b^6-192\,A^2\,C\,a^7\,b^7+240\,A^2\,C\,a^6\,b^8-288\,A^2\,C\,a^5\,b^9+288\,A^2\,C\,a^4\,b^{10}-288\,A^2\,C\,a^3\,b^{11}+192\,A^2\,C\,a^2\,b^{12}-24\,A\,B^2\,a^9\,b^5+48\,A\,B^2\,a^8\,b^6-120\,A\,B^2\,a^7\,b^7+168\,A\,B^2\,a^6\,b^8-264\,A\,B^2\,a^5\,b^9+288\,A\,B^2\,a^4\,b^{10}-288\,A\,B^2\,a^3\,b^{11}+192\,A\,B^2\,a^2\,b^{12}+48\,A\,B\,C\,a^{10}\,b^4-96\,A\,B\,C\,a^9\,b^5+240\,A\,B\,C\,a^8\,b^6-336\,A\,B\,C\,a^7\,b^7+528\,A\,B\,C\,a^6\,b^8-576\,A\,B\,C\,a^5\,b^9+576\,A\,B\,C\,a^4\,b^{10}-384\,A\,B\,C\,a^3\,b^{11}-24\,A\,C^2\,a^{11}\,b^3+48\,A\,C^2\,a^{10}\,b^4-120\,A\,C^2\,a^9\,b^5+168\,A\,C^2\,a^8\,b^6-264\,A\,C^2\,a^7\,b^7+288\,A\,C^2\,a^6\,b^8-288\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}+16\,B^3\,a^8\,b^6-32\,B^3\,a^7\,b^7+80\,B^3\,a^6\,b^8-96\,B^3\,a^5\,b^9+96\,B^3\,a^4\,b^{10}-64\,B^3\,a^3\,b^{11}-48\,B^2\,C\,a^9\,b^5+96\,B^2\,C\,a^8\,b^6-240\,B^2\,C\,a^7\,b^7+288\,B^2\,C\,a^6\,b^8-288\,B^2\,C\,a^5\,b^9+192\,B^2\,C\,a^4\,b^{10}+48\,B\,C^2\,a^{10}\,b^4-96\,B\,C^2\,a^9\,b^5+240\,B\,C^2\,a^8\,b^6-288\,B\,C^2\,a^7\,b^7+288\,B\,C^2\,a^6\,b^8-192\,B\,C^2\,a^5\,b^9-16\,C^3\,a^{11}\,b^3+32\,C^3\,a^{10}\,b^4-80\,C^3\,a^9\,b^5+96\,C^3\,a^8\,b^6-96\,C^3\,a^7\,b^7+64\,C^3\,a^6\,b^8}{a^{12}}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{a^5}-\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)}{a^5}}\right)\,\left(a^2\,\left(\frac{A\,b^2\,1{}\mathrm{i}}{2}+C\,b^2\,1{}\mathrm{i}\right)+A\,b^4\,1{}\mathrm{i}+a^4\,\left(\frac{A\,3{}\mathrm{i}}{8}+\frac{C\,1{}\mathrm{i}}{2}\right)-B\,a\,b^3\,1{}\mathrm{i}-\frac{B\,a^3\,b\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{-9\,A^3\,a^9\,b^5+18\,A^3\,a^8\,b^6-33\,A^3\,a^7\,b^7+48\,A^3\,a^6\,b^8-88\,A^3\,a^5\,b^9+104\,A^3\,a^4\,b^{10}-104\,A^3\,a^3\,b^{11}+96\,A^3\,a^2\,b^{12}-96\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+9\,A^2\,B\,a^{10}\,b^4-18\,A^2\,B\,a^9\,b^5+57\,A^2\,B\,a^8\,b^6-96\,A^2\,B\,a^7\,b^7+192\,A^2\,B\,a^6\,b^8-240\,A^2\,B\,a^5\,b^9+288\,A^2\,B\,a^4\,b^{10}-288\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-192\,A^2\,B\,a\,b^{13}-9\,A^2\,C\,a^{11}\,b^3+18\,A^2\,C\,a^{10}\,b^4-57\,A^2\,C\,a^9\,b^5+96\,A^2\,C\,a^8\,b^6-192\,A^2\,C\,a^7\,b^7+240\,A^2\,C\,a^6\,b^8-288\,A^2\,C\,a^5\,b^9+288\,A^2\,C\,a^4\,b^{10}-288\,A^2\,C\,a^3\,b^{11}+192\,A^2\,C\,a^2\,b^{12}-24\,A\,B^2\,a^9\,b^5+48\,A\,B^2\,a^8\,b^6-120\,A\,B^2\,a^7\,b^7+168\,A\,B^2\,a^6\,b^8-264\,A\,B^2\,a^5\,b^9+288\,A\,B^2\,a^4\,b^{10}-288\,A\,B^2\,a^3\,b^{11}+192\,A\,B^2\,a^2\,b^{12}+48\,A\,B\,C\,a^{10}\,b^4-96\,A\,B\,C\,a^9\,b^5+240\,A\,B\,C\,a^8\,b^6-336\,A\,B\,C\,a^7\,b^7+528\,A\,B\,C\,a^6\,b^8-576\,A\,B\,C\,a^5\,b^9+576\,A\,B\,C\,a^4\,b^{10}-384\,A\,B\,C\,a^3\,b^{11}-24\,A\,C^2\,a^{11}\,b^3+48\,A\,C^2\,a^{10}\,b^4-120\,A\,C^2\,a^9\,b^5+168\,A\,C^2\,a^8\,b^6-264\,A\,C^2\,a^7\,b^7+288\,A\,C^2\,a^6\,b^8-288\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}+16\,B^3\,a^8\,b^6-32\,B^3\,a^7\,b^7+80\,B^3\,a^6\,b^8-96\,B^3\,a^5\,b^9+96\,B^3\,a^4\,b^{10}-64\,B^3\,a^3\,b^{11}-48\,B^2\,C\,a^9\,b^5+96\,B^2\,C\,a^8\,b^6-240\,B^2\,C\,a^7\,b^7+288\,B^2\,C\,a^6\,b^8-288\,B^2\,C\,a^5\,b^9+192\,B^2\,C\,a^4\,b^{10}+48\,B\,C^2\,a^{10}\,b^4-96\,B\,C^2\,a^9\,b^5+240\,B\,C^2\,a^8\,b^6-288\,B\,C^2\,a^7\,b^7+288\,B\,C^2\,a^6\,b^8-192\,B\,C^2\,a^5\,b^9-16\,C^3\,a^{11}\,b^3+32\,C^3\,a^{10}\,b^4-80\,C^3\,a^9\,b^5+96\,C^3\,a^8\,b^6-96\,C^3\,a^7\,b^7+64\,C^3\,a^6\,b^8}{a^{12}}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^7*(5*A*a^3 + 8*A*b^3 - 8*B*a^3 + 4*C*a^3 + 4*A*a*b^2 + 8*A*a^2*b - 8*B*a*b^2 - 4*B*a^2*b + 8*C*a^2*b))/(4*a^4) + (tan(c/2 + (d*x)/2)^3*(9*A*a^3 + 72*A*b^3 - 40*B*a^3 - 12*C*a^3 - 12*A*a*b^2 + 40*A*a^2*b - 72*B*a*b^2 + 12*B*a^2*b + 72*C*a^2*b))/(12*a^4) + (tan(c/2 + (d*x)/2)^5*(72*A*b^3 - 9*A*a^3 - 40*B*a^3 + 12*C*a^3 + 12*A*a*b^2 + 40*A*a^2*b - 72*B*a*b^2 - 12*B*a^2*b + 72*C*a^2*b))/(12*a^4) - (tan(c/2 + (d*x)/2)*(5*A*a^3 - 8*A*b^3 + 8*B*a^3 + 4*C*a^3 + 4*A*a*b^2 - 8*A*a^2*b + 8*B*a*b^2 - 4*B*a^2*b - 8*C*a^2*b))/(4*a^4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atan(((((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/a^5)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2)*1i)/a^5 + (((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/a^5)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2)*1i)/a^5)/((64*A^3*b^14 - 96*A^3*a*b^13 + 96*A^3*a^2*b^12 - 104*A^3*a^3*b^11 + 104*A^3*a^4*b^10 - 88*A^3*a^5*b^9 + 48*A^3*a^6*b^8 - 33*A^3*a^7*b^7 + 18*A^3*a^8*b^6 - 9*A^3*a^9*b^5 - 64*B^3*a^3*b^11 + 96*B^3*a^4*b^10 - 96*B^3*a^5*b^9 + 80*B^3*a^6*b^8 - 32*B^3*a^7*b^7 + 16*B^3*a^8*b^6 + 64*C^3*a^6*b^8 - 96*C^3*a^7*b^7 + 96*C^3*a^8*b^6 - 80*C^3*a^9*b^5 + 32*C^3*a^10*b^4 - 16*C^3*a^11*b^3 - 192*A^2*B*a*b^13 + 192*A*B^2*a^2*b^12 - 288*A*B^2*a^3*b^11 + 288*A*B^2*a^4*b^10 - 264*A*B^2*a^5*b^9 + 168*A*B^2*a^6*b^8 - 120*A*B^2*a^7*b^7 + 48*A*B^2*a^8*b^6 - 24*A*B^2*a^9*b^5 + 288*A^2*B*a^2*b^12 - 288*A^2*B*a^3*b^11 + 288*A^2*B*a^4*b^10 - 240*A^2*B*a^5*b^9 + 192*A^2*B*a^6*b^8 - 96*A^2*B*a^7*b^7 + 57*A^2*B*a^8*b^6 - 18*A^2*B*a^9*b^5 + 9*A^2*B*a^10*b^4 + 192*A*C^2*a^4*b^10 - 288*A*C^2*a^5*b^9 + 288*A*C^2*a^6*b^8 - 264*A*C^2*a^7*b^7 + 168*A*C^2*a^8*b^6 - 120*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 - 24*A*C^2*a^11*b^3 + 192*A^2*C*a^2*b^12 - 288*A^2*C*a^3*b^11 + 288*A^2*C*a^4*b^10 - 288*A^2*C*a^5*b^9 + 240*A^2*C*a^6*b^8 - 192*A^2*C*a^7*b^7 + 96*A^2*C*a^8*b^6 - 57*A^2*C*a^9*b^5 + 18*A^2*C*a^10*b^4 - 9*A^2*C*a^11*b^3 - 192*B*C^2*a^5*b^9 + 288*B*C^2*a^6*b^8 - 288*B*C^2*a^7*b^7 + 240*B*C^2*a^8*b^6 - 96*B*C^2*a^9*b^5 + 48*B*C^2*a^10*b^4 + 192*B^2*C*a^4*b^10 - 288*B^2*C*a^5*b^9 + 288*B^2*C*a^6*b^8 - 240*B^2*C*a^7*b^7 + 96*B^2*C*a^8*b^6 - 48*B^2*C*a^9*b^5 - 384*A*B*C*a^3*b^11 + 576*A*B*C*a^4*b^10 - 576*A*B*C*a^5*b^9 + 528*A*B*C*a^6*b^8 - 336*A*B*C*a^7*b^7 + 240*A*B*C*a^8*b^6 - 96*A*B*C*a^9*b^5 + 48*A*B*C*a^10*b^4)/a^12 + (((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/a^5)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/a^5 - (((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/(2*a^13))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/a^5)*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2))/a^5))*(a^2*((A*b^2*1i)/2 + C*b^2*1i) + A*b^4*1i + a^4*((A*3i)/8 + (C*1i)/2) - B*a*b^3*1i - (B*a^3*b*1i)/2)*2i)/(a^5*d) - (b^3*atan(((b^3*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (b^3*((a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^7 - a^5*b^2) + (b^3*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (b^3*((a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^7 - a^5*b^2))/((64*A^3*b^14 - 96*A^3*a*b^13 + 96*A^3*a^2*b^12 - 104*A^3*a^3*b^11 + 104*A^3*a^4*b^10 - 88*A^3*a^5*b^9 + 48*A^3*a^6*b^8 - 33*A^3*a^7*b^7 + 18*A^3*a^8*b^6 - 9*A^3*a^9*b^5 - 64*B^3*a^3*b^11 + 96*B^3*a^4*b^10 - 96*B^3*a^5*b^9 + 80*B^3*a^6*b^8 - 32*B^3*a^7*b^7 + 16*B^3*a^8*b^6 + 64*C^3*a^6*b^8 - 96*C^3*a^7*b^7 + 96*C^3*a^8*b^6 - 80*C^3*a^9*b^5 + 32*C^3*a^10*b^4 - 16*C^3*a^11*b^3 - 192*A^2*B*a*b^13 + 192*A*B^2*a^2*b^12 - 288*A*B^2*a^3*b^11 + 288*A*B^2*a^4*b^10 - 264*A*B^2*a^5*b^9 + 168*A*B^2*a^6*b^8 - 120*A*B^2*a^7*b^7 + 48*A*B^2*a^8*b^6 - 24*A*B^2*a^9*b^5 + 288*A^2*B*a^2*b^12 - 288*A^2*B*a^3*b^11 + 288*A^2*B*a^4*b^10 - 240*A^2*B*a^5*b^9 + 192*A^2*B*a^6*b^8 - 96*A^2*B*a^7*b^7 + 57*A^2*B*a^8*b^6 - 18*A^2*B*a^9*b^5 + 9*A^2*B*a^10*b^4 + 192*A*C^2*a^4*b^10 - 288*A*C^2*a^5*b^9 + 288*A*C^2*a^6*b^8 - 264*A*C^2*a^7*b^7 + 168*A*C^2*a^8*b^6 - 120*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 - 24*A*C^2*a^11*b^3 + 192*A^2*C*a^2*b^12 - 288*A^2*C*a^3*b^11 + 288*A^2*C*a^4*b^10 - 288*A^2*C*a^5*b^9 + 240*A^2*C*a^6*b^8 - 192*A^2*C*a^7*b^7 + 96*A^2*C*a^8*b^6 - 57*A^2*C*a^9*b^5 + 18*A^2*C*a^10*b^4 - 9*A^2*C*a^11*b^3 - 192*B*C^2*a^5*b^9 + 288*B*C^2*a^6*b^8 - 288*B*C^2*a^7*b^7 + 240*B*C^2*a^8*b^6 - 96*B*C^2*a^9*b^5 + 48*B*C^2*a^10*b^4 + 192*B^2*C*a^4*b^10 - 288*B^2*C*a^5*b^9 + 288*B^2*C*a^6*b^8 - 240*B^2*C*a^7*b^7 + 96*B^2*C*a^8*b^6 - 48*B^2*C*a^9*b^5 - 384*A*B*C*a^3*b^11 + 576*A*B*C*a^4*b^10 - 576*A*B*C*a^5*b^9 + 528*A*B*C*a^6*b^8 - 336*A*B*C*a^7*b^7 + 240*A*B*C*a^8*b^6 - 96*A*B*C*a^9*b^5 + 48*A*B*C*a^10*b^4)/a^12 + (b^3*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (b^3*((a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2) - (b^3*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (b^3*((a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2)))*((a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^7 - a^5*b^2))","B"
908,1,11687,407,17.877652,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b/cos(c + d*x))^2),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,b^5-3\,B\,b^5-72\,C\,a^5-6\,A\,b^5+6\,A\,a^2\,b^3-36\,A\,a^3\,b^2-33\,B\,a^2\,b^3-9\,B\,a^3\,b^2-14\,C\,a^2\,b^3+38\,C\,a^3\,b^2+18\,A\,a\,b^4+9\,B\,a\,b^4+54\,B\,a^4\,b+16\,C\,a\,b^4+12\,C\,a^4\,b\right)}{3\,\left(a\,b^4-b^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,b^5-B\,b^5+8\,C\,a^5+2\,C\,b^5-2\,A\,a^2\,b^3+4\,A\,a^3\,b^2+5\,B\,a^2\,b^3+3\,B\,a^3\,b^2+2\,C\,a^2\,b^3-6\,C\,a^3\,b^2-2\,A\,a\,b^4-3\,B\,a\,b^4-6\,B\,a^4\,b-4\,C\,a^4\,b\right)}{\left(a\,b^4-b^5\right)\,\left(a+b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^5+B\,b^5-8\,C\,a^5+2\,C\,b^5-2\,A\,a^2\,b^3-4\,A\,a^3\,b^2-5\,B\,a^2\,b^3+3\,B\,a^3\,b^2+2\,C\,a^2\,b^3+6\,C\,a^3\,b^2+2\,A\,a\,b^4-3\,B\,a\,b^4+6\,B\,a^4\,b-4\,C\,a^4\,b\right)}{\left(a\,b^4-b^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,B\,b^5-6\,A\,b^5+72\,C\,a^5+2\,C\,b^5+6\,A\,a^2\,b^3+36\,A\,a^3\,b^2+33\,B\,a^2\,b^3-9\,B\,a^3\,b^2-14\,C\,a^2\,b^3-38\,C\,a^3\,b^2-18\,A\,a\,b^4+9\,B\,a\,b^4-54\,B\,a^4\,b-16\,C\,a\,b^4+12\,C\,a^4\,b\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,b-4\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-4\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)\,1{}\mathrm{i}}{b^5}}{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3}{2}-4\,C\,a^3-b^2\,\left(2\,A\,a+C\,a\right)+3\,B\,a^2\,b\right)}{b^5}-\frac{16\,\left(32\,A^3\,a^8\,b^6-16\,A^3\,a^7\,b^7-80\,A^3\,a^6\,b^8+24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}-144\,A^2\,B\,a^9\,b^5+72\,A^2\,B\,a^8\,b^6+336\,A^2\,B\,a^7\,b^7-108\,A^2\,B\,a^6\,b^8-168\,A^2\,B\,a^5\,b^9+6\,A^2\,B\,a^4\,b^{10}-24\,A^2\,B\,a^3\,b^{11}+192\,A^2\,C\,a^{10}\,b^4-96\,A^2\,C\,a^9\,b^5-432\,A^2\,C\,a^8\,b^6+144\,A^2\,C\,a^7\,b^7+192\,A^2\,C\,a^6\,b^8-12\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}+216\,A\,B^2\,a^{10}\,b^4-108\,A\,B^2\,a^9\,b^5-468\,A\,B^2\,a^8\,b^6+162\,A\,B^2\,a^7\,b^7+186\,A\,B^2\,a^6\,b^8-15\,A\,B^2\,a^5\,b^9+63\,A\,B^2\,a^4\,b^{10}-3\,A\,B^2\,a^3\,b^{11}+3\,A\,B^2\,a^2\,b^{12}-576\,A\,B\,C\,a^{11}\,b^3+288\,A\,B\,C\,a^{10}\,b^4+1200\,A\,B\,C\,a^9\,b^5-432\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7+48\,A\,B\,C\,a^6\,b^8-204\,A\,B\,C\,a^5\,b^9+12\,A\,B\,C\,a^4\,b^{10}-12\,A\,B\,C\,a^3\,b^{11}+384\,A\,C^2\,a^{12}\,b^2-192\,A\,C^2\,a^{11}\,b^3-768\,A\,C^2\,a^{10}\,b^4+288\,A\,C^2\,a^9\,b^5+216\,A\,C^2\,a^8\,b^6-36\,A\,C^2\,a^7\,b^7+156\,A\,C^2\,a^6\,b^8-12\,A\,C^2\,a^5\,b^9+12\,A\,C^2\,a^4\,b^{10}-108\,B^3\,a^{11}\,b^3+54\,B^3\,a^{10}\,b^4+216\,B^3\,a^9\,b^5-81\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7+9\,B^3\,a^6\,b^8-41\,B^3\,a^5\,b^9+4\,B^3\,a^4\,b^{10}-4\,B^3\,a^3\,b^{11}+432\,B^2\,C\,a^{12}\,b^2-216\,B^2\,C\,a^{11}\,b^3-828\,B^2\,C\,a^{10}\,b^4+324\,B^2\,C\,a^9\,b^5+192\,B^2\,C\,a^8\,b^6-39\,B^2\,C\,a^7\,b^7+183\,B^2\,C\,a^6\,b^8-21\,B^2\,C\,a^5\,b^9+21\,B^2\,C\,a^4\,b^{10}-576\,B\,C^2\,a^{13}\,b+288\,B\,C^2\,a^{12}\,b^2+1056\,B\,C^2\,a^{11}\,b^3-432\,B\,C^2\,a^{10}\,b^4-180\,B\,C^2\,a^9\,b^5+54\,B\,C^2\,a^8\,b^6-264\,B\,C^2\,a^7\,b^7+36\,B\,C^2\,a^6\,b^8-36\,B\,C^2\,a^5\,b^9+256\,C^3\,a^{14}-128\,C^3\,a^{13}\,b-448\,C^3\,a^{12}\,b^2+192\,C^3\,a^{11}\,b^3+48\,C^3\,a^{10}\,b^4-24\,C^3\,a^9\,b^5+124\,C^3\,a^8\,b^6-20\,C^3\,a^7\,b^7+20\,C^3\,a^6\,b^8\right)}{-a^3\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b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}{\frac{16\,\left(32\,A^3\,a^8\,b^6-16\,A^3\,a^7\,b^7-80\,A^3\,a^6\,b^8+24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}-144\,A^2\,B\,a^9\,b^5+72\,A^2\,B\,a^8\,b^6+336\,A^2\,B\,a^7\,b^7-108\,A^2\,B\,a^6\,b^8-168\,A^2\,B\,a^5\,b^9+6\,A^2\,B\,a^4\,b^{10}-24\,A^2\,B\,a^3\,b^{11}+192\,A^2\,C\,a^{10}\,b^4-96\,A^2\,C\,a^9\,b^5-432\,A^2\,C\,a^8\,b^6+144\,A^2\,C\,a^7\,b^7+192\,A^2\,C\,a^6\,b^8-12\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}+216\,A\,B^2\,a^{10}\,b^4-108\,A\,B^2\,a^9\,b^5-468\,A\,B^2\,a^8\,b^6+162\,A\,B^2\,a^7\,b^7+186\,A\,B^2\,a^6\,b^8-15\,A\,B^2\,a^5\,b^9+63\,A\,B^2\,a^4\,b^{10}-3\,A\,B^2\,a^3\,b^{11}+3\,A\,B^2\,a^2\,b^{12}-576\,A\,B\,C\,a^{11}\,b^3+288\,A\,B\,C\,a^{10}\,b^4+1200\,A\,B\,C\,a^9\,b^5-432\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7+48\,A\,B\,C\,a^6\,b^8-204\,A\,B\,C\,a^5\,b^9+12\,A\,B\,C\,a^4\,b^{10}-12\,A\,B\,C\,a^3\,b^{11}+384\,A\,C^2\,a^{12}\,b^2-192\,A\,C^2\,a^{11}\,b^3-768\,A\,C^2\,a^{10}\,b^4+288\,A\,C^2\,a^9\,b^5+216\,A\,C^2\,a^8\,b^6-36\,A\,C^2\,a^7\,b^7+156\,A\,C^2\,a^6\,b^8-12\,A\,C^2\,a^5\,b^9+12\,A\,C^2\,a^4\,b^{10}-108\,B^3\,a^{11}\,b^3+54\,B^3\,a^{10}\,b^4+216\,B^3\,a^9\,b^5-81\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7+9\,B^3\,a^6\,b^8-41\,B^3\,a^5\,b^9+4\,B^3\,a^4\,b^{10}-4\,B^3\,a^3\,b^{11}+432\,B^2\,C\,a^{12}\,b^2-216\,B^2\,C\,a^{11}\,b^3-828\,B^2\,C\,a^{10}\,b^4+324\,B^2\,C\,a^9\,b^5+192\,B^2\,C\,a^8\,b^6-39\,B^2\,C\,a^7\,b^7+183\,B^2\,C\,a^6\,b^8-21\,B^2\,C\,a^5\,b^9+21\,B^2\,C\,a^4\,b^{10}-576\,B\,C^2\,a^{13}\,b+288\,B\,C^2\,a^{12}\,b^2+1056\,B\,C^2\,a^{11}\,b^3-432\,B\,C^2\,a^{10}\,b^4-180\,B\,C^2\,a^9\,b^5+54\,B\,C^2\,a^8\,b^6-264\,B\,C^2\,a^7\,b^7+36\,B\,C^2\,a^6\,b^8-36\,B\,C^2\,a^5\,b^9+256\,C^3\,a^{14}-128\,C^3\,a^{13}\,b-448\,C^3\,a^{12}\,b^2+192\,C^3\,a^{11}\,b^3+48\,C^3\,a^{10}\,b^4-24\,C^3\,a^9\,b^5+124\,C^3\,a^8\,b^6-20\,C^3\,a^7\,b^7+20\,C^3\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}","Not used",1,"(atan(((((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*tan(c/2 + (d*x)/2)*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b))/b^5 - (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*1i)/b^5 - (((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*tan(c/2 + (d*x)/2)*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b))/b^5 + (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*1i)/b^5)/((((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*tan(c/2 + (d*x)/2)*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b))/b^5 - (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b))/b^5 - (16*(256*C^3*a^14 - 128*C^3*a^13*b + 48*A^3*a^4*b^10 + 24*A^3*a^5*b^9 - 80*A^3*a^6*b^8 - 16*A^3*a^7*b^7 + 32*A^3*a^8*b^6 - 4*B^3*a^3*b^11 + 4*B^3*a^4*b^10 - 41*B^3*a^5*b^9 + 9*B^3*a^6*b^8 - 63*B^3*a^7*b^7 - 81*B^3*a^8*b^6 + 216*B^3*a^9*b^5 + 54*B^3*a^10*b^4 - 108*B^3*a^11*b^3 + 20*C^3*a^6*b^8 - 20*C^3*a^7*b^7 + 124*C^3*a^8*b^6 - 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 + 192*C^3*a^11*b^3 - 448*C^3*a^12*b^2 - 576*B*C^2*a^13*b + 3*A*B^2*a^2*b^12 - 3*A*B^2*a^3*b^11 + 63*A*B^2*a^4*b^10 - 15*A*B^2*a^5*b^9 + 186*A*B^2*a^6*b^8 + 162*A*B^2*a^7*b^7 - 468*A*B^2*a^8*b^6 - 108*A*B^2*a^9*b^5 + 216*A*B^2*a^10*b^4 - 24*A^2*B*a^3*b^11 + 6*A^2*B*a^4*b^10 - 168*A^2*B*a^5*b^9 - 108*A^2*B*a^6*b^8 + 336*A^2*B*a^7*b^7 + 72*A^2*B*a^8*b^6 - 144*A^2*B*a^9*b^5 + 12*A*C^2*a^4*b^10 - 12*A*C^2*a^5*b^9 + 156*A*C^2*a^6*b^8 - 36*A*C^2*a^7*b^7 + 216*A*C^2*a^8*b^6 + 288*A*C^2*a^9*b^5 - 768*A*C^2*a^10*b^4 - 192*A*C^2*a^11*b^3 + 384*A*C^2*a^12*b^2 + 48*A^2*C*a^4*b^10 - 12*A^2*C*a^5*b^9 + 192*A^2*C*a^6*b^8 + 144*A^2*C*a^7*b^7 - 432*A^2*C*a^8*b^6 - 96*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4 - 36*B*C^2*a^5*b^9 + 36*B*C^2*a^6*b^8 - 264*B*C^2*a^7*b^7 + 54*B*C^2*a^8*b^6 - 180*B*C^2*a^9*b^5 - 432*B*C^2*a^10*b^4 + 1056*B*C^2*a^11*b^3 + 288*B*C^2*a^12*b^2 + 21*B^2*C*a^4*b^10 - 21*B^2*C*a^5*b^9 + 183*B^2*C*a^6*b^8 - 39*B^2*C*a^7*b^7 + 192*B^2*C*a^8*b^6 + 324*B^2*C*a^9*b^5 - 828*B^2*C*a^10*b^4 - 216*B^2*C*a^11*b^3 + 432*B^2*C*a^12*b^2 - 12*A*B*C*a^3*b^11 + 12*A*B*C*a^4*b^10 - 204*A*B*C*a^5*b^9 + 48*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 - 432*A*B*C*a^8*b^6 + 1200*A*B*C*a^9*b^5 + 288*A*B*C*a^10*b^4 - 576*A*B*C*a^11*b^3))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*tan(c/2 + (d*x)/2)*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b))/b^5 + (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b))/b^5))*((B*b^3)/2 - 4*C*a^3 - b^2*(2*A*a + C*a) + 3*B*a^2*b)*2i)/(b^5*d) - ((tan(c/2 + (d*x)/2)^5*(2*C*b^5 - 3*B*b^5 - 72*C*a^5 - 6*A*b^5 + 6*A*a^2*b^3 - 36*A*a^3*b^2 - 33*B*a^2*b^3 - 9*B*a^3*b^2 - 14*C*a^2*b^3 + 38*C*a^3*b^2 + 18*A*a*b^4 + 9*B*a*b^4 + 54*B*a^4*b + 16*C*a*b^4 + 12*C*a^4*b))/(3*(a*b^4 - b^5)*(a + b)) + (tan(c/2 + (d*x)/2)^7*(2*A*b^5 - B*b^5 + 8*C*a^5 + 2*C*b^5 - 2*A*a^2*b^3 + 4*A*a^3*b^2 + 5*B*a^2*b^3 + 3*B*a^3*b^2 + 2*C*a^2*b^3 - 6*C*a^3*b^2 - 2*A*a*b^4 - 3*B*a*b^4 - 6*B*a^4*b - 4*C*a^4*b))/((a*b^4 - b^5)*(a + b)) + (tan(c/2 + (d*x)/2)*(2*A*b^5 + B*b^5 - 8*C*a^5 + 2*C*b^5 - 2*A*a^2*b^3 - 4*A*a^3*b^2 - 5*B*a^2*b^3 + 3*B*a^3*b^2 + 2*C*a^2*b^3 + 6*C*a^3*b^2 + 2*A*a*b^4 - 3*B*a*b^4 + 6*B*a^4*b - 4*C*a^4*b))/((a*b^4 - b^5)*(a + b)) + (tan(c/2 + (d*x)/2)^3*(3*B*b^5 - 6*A*b^5 + 72*C*a^5 + 2*C*b^5 + 6*A*a^2*b^3 + 36*A*a^3*b^2 + 33*B*a^2*b^3 - 9*B*a^3*b^2 - 14*C*a^2*b^3 - 38*C*a^3*b^2 - 18*A*a*b^4 + 9*B*a*b^4 - 54*B*a^4*b - 16*C*a*b^4 + 12*C*a^4*b))/(3*b^4*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^8*(a - b) - tan(c/2 + (d*x)/2)^2*(4*a + 2*b) - tan(c/2 + (d*x)/2)^6*(4*a - 2*b) + 6*a*tan(c/2 + (d*x)/2)^4)) + (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b)*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b)*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))/((16*(256*C^3*a^14 - 128*C^3*a^13*b + 48*A^3*a^4*b^10 + 24*A^3*a^5*b^9 - 80*A^3*a^6*b^8 - 16*A^3*a^7*b^7 + 32*A^3*a^8*b^6 - 4*B^3*a^3*b^11 + 4*B^3*a^4*b^10 - 41*B^3*a^5*b^9 + 9*B^3*a^6*b^8 - 63*B^3*a^7*b^7 - 81*B^3*a^8*b^6 + 216*B^3*a^9*b^5 + 54*B^3*a^10*b^4 - 108*B^3*a^11*b^3 + 20*C^3*a^6*b^8 - 20*C^3*a^7*b^7 + 124*C^3*a^8*b^6 - 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 + 192*C^3*a^11*b^3 - 448*C^3*a^12*b^2 - 576*B*C^2*a^13*b + 3*A*B^2*a^2*b^12 - 3*A*B^2*a^3*b^11 + 63*A*B^2*a^4*b^10 - 15*A*B^2*a^5*b^9 + 186*A*B^2*a^6*b^8 + 162*A*B^2*a^7*b^7 - 468*A*B^2*a^8*b^6 - 108*A*B^2*a^9*b^5 + 216*A*B^2*a^10*b^4 - 24*A^2*B*a^3*b^11 + 6*A^2*B*a^4*b^10 - 168*A^2*B*a^5*b^9 - 108*A^2*B*a^6*b^8 + 336*A^2*B*a^7*b^7 + 72*A^2*B*a^8*b^6 - 144*A^2*B*a^9*b^5 + 12*A*C^2*a^4*b^10 - 12*A*C^2*a^5*b^9 + 156*A*C^2*a^6*b^8 - 36*A*C^2*a^7*b^7 + 216*A*C^2*a^8*b^6 + 288*A*C^2*a^9*b^5 - 768*A*C^2*a^10*b^4 - 192*A*C^2*a^11*b^3 + 384*A*C^2*a^12*b^2 + 48*A^2*C*a^4*b^10 - 12*A^2*C*a^5*b^9 + 192*A^2*C*a^6*b^8 + 144*A^2*C*a^7*b^7 - 432*A^2*C*a^8*b^6 - 96*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4 - 36*B*C^2*a^5*b^9 + 36*B*C^2*a^6*b^8 - 264*B*C^2*a^7*b^7 + 54*B*C^2*a^8*b^6 - 180*B*C^2*a^9*b^5 - 432*B*C^2*a^10*b^4 + 1056*B*C^2*a^11*b^3 + 288*B*C^2*a^12*b^2 + 21*B^2*C*a^4*b^10 - 21*B^2*C*a^5*b^9 + 183*B^2*C*a^6*b^8 - 39*B^2*C*a^7*b^7 + 192*B^2*C*a^8*b^6 + 324*B^2*C*a^9*b^5 - 828*B^2*C*a^10*b^4 - 216*B^2*C*a^11*b^3 + 432*B^2*C*a^12*b^2 - 12*A*B*C*a^3*b^11 + 12*A*B*C*a^4*b^10 - 204*A*B*C*a^5*b^9 + 48*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 - 432*A*B*C*a^8*b^6 + 1200*A*B*C*a^9*b^5 + 288*A*B*C*a^10*b^4 - 576*A*B*C*a^11*b^3))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*a^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b)*2i)/(d*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))","B"
909,1,9931,312,17.546407,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^2),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^4-2\,B\,b^4+C\,b^4+2\,A\,a^2\,b^2+2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b+3\,C\,a\,b^3-3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,C\,a^4-C\,b^4+2\,A\,a^2\,b^2-3\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b\right)}{b\,\left(a\,b^2-b^3\right)\,\left(a+b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4+6\,C\,a^4+C\,b^4+2\,A\,a^2\,b^2-2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b-3\,C\,a\,b^3+3\,C\,a^3\,b\right)}{b^3\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^4}-\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}-24\,A^2\,B\,a^6\,b^5+20\,A^2\,B\,a^5\,b^6+68\,A^2\,B\,a^4\,b^7-36\,A^2\,B\,a^3\,b^8-44\,A^2\,B\,a^2\,b^9+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+48\,A\,B^2\,a^7\,b^4-32\,A\,B^2\,a^6\,b^5-128\,A\,B^2\,a^5\,b^6+52\,A\,B^2\,a^4\,b^7+80\,A\,B^2\,a^3\,b^8-144\,A\,B\,C\,a^8\,b^3+96\,A\,B\,C\,a^7\,b^4+360\,A\,B\,C\,a^6\,b^5-152\,A\,B\,C\,a^5\,b^6-188\,A\,B\,C\,a^4\,b^7+4\,A\,B\,C\,a^3\,b^8-28\,A\,B\,C\,a^2\,b^9+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}+\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^4}}\right)\,\left(3\,C\,a^2-2\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}-24\,A^2\,B\,a^6\,b^5+20\,A^2\,B\,a^5\,b^6+68\,A^2\,B\,a^4\,b^7-36\,A^2\,B\,a^3\,b^8-44\,A^2\,B\,a^2\,b^9+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+48\,A\,B^2\,a^7\,b^4-32\,A\,B^2\,a^6\,b^5-128\,A\,B^2\,a^5\,b^6+52\,A\,B^2\,a^4\,b^7+80\,A\,B^2\,a^3\,b^8-144\,A\,B\,C\,a^8\,b^3+96\,A\,B\,C\,a^7\,b^4+360\,A\,B\,C\,a^6\,b^5-152\,A\,B\,C\,a^5\,b^6-188\,A\,B\,C\,a^4\,b^7+4\,A\,B\,C\,a^3\,b^8-28\,A\,B\,C\,a^2\,b^9+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"(atan(((((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b))/b^4 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*1i)/b^4 - (((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b))/b^4 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*1i)/b^4)/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 216*B*C^2*a^10*b + 80*A*B^2*a^3*b^8 + 52*A*B^2*a^4*b^7 - 128*A*B^2*a^5*b^6 - 32*A*B^2*a^6*b^5 + 48*A*B^2*a^7*b^4 - 44*A^2*B*a^2*b^9 - 36*A^2*B*a^3*b^8 + 68*A^2*B*a^4*b^7 + 20*A^2*B*a^5*b^6 - 24*A^2*B*a^6*b^5 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4 - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2 - 28*A*B*C*a^2*b^9 + 4*A*B*C*a^3*b^8 - 188*A*B*C*a^4*b^7 - 152*A*B*C*a^5*b^6 + 360*A*B*C*a^6*b^5 + 96*A*B*C*a^7*b^4 - 144*A*B*C*a^8*b^3))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b))/b^4 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b))/b^4 + (((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b))/b^4 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b))/b^4))*(3*C*a^2 + b^2*(A + C/2) - 2*B*a*b)*2i)/(b^4*d) - ((tan(c/2 + (d*x)/2)^5*(6*C*a^4 - 2*B*b^4 + C*b^4 + 2*A*a^2*b^2 + 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b + 3*C*a*b^3 - 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(6*C*a^4 - C*b^4 + 2*A*a^2*b^2 - 3*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b))/(b*(a*b^2 - b^3)*(a + b)) + (tan(c/2 + (d*x)/2)*(2*B*b^4 + 6*C*a^4 + C*b^4 + 2*A*a^2*b^2 - 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b - 3*C*a*b^3 + 3*C*a^3*b))/(b^3*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(3*a + b) - tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 216*B*C^2*a^10*b + 80*A*B^2*a^3*b^8 + 52*A*B^2*a^4*b^7 - 128*A*B^2*a^5*b^6 - 32*A*B^2*a^6*b^5 + 48*A*B^2*a^7*b^4 - 44*A^2*B*a^2*b^9 - 36*A^2*B*a^3*b^8 + 68*A^2*B*a^4*b^7 + 20*A^2*B*a^5*b^6 - 24*A^2*B*a^6*b^5 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4 - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2 - 28*A*B*C*a^2*b^9 + 4*A*B*C*a^3*b^8 - 188*A*B*C*a^4*b^7 - 152*A*B*C*a^5*b^6 + 360*A*B*C*a^6*b^5 + 96*A*B*C*a^7*b^4 - 144*A*B*C*a^8*b^3))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*((a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
910,1,6421,177,14.163607,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^2),x)","\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a^3-C\,b^3+A\,a\,b^2-B\,a^2\,b-C\,a\,b^2+C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^3+C\,b^3+A\,a\,b^2-B\,a^2\,b-C\,a\,b^2-C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}\right)\,1{}\mathrm{i}}{b^3}-\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}\right)\,1{}\mathrm{i}}{b^3}}{\frac{64\,\left(-A^2\,B\,b^8+2\,A^2\,C\,a\,b^7-A\,B^2\,a^3\,b^5-A\,B^2\,a^2\,b^6+3\,A\,B^2\,a\,b^7+A\,B^2\,b^8+4\,A\,B\,C\,a^4\,b^4+4\,A\,B\,C\,a^3\,b^5-10\,A\,B\,C\,a^2\,b^6-4\,A\,B\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6-B^3\,a^5\,b^3+B^3\,a^4\,b^4+3\,B^3\,a^3\,b^5-2\,B^3\,a^2\,b^6-2\,B^3\,a\,b^7+6\,B^2\,C\,a^6\,b^2-5\,B^2\,C\,a^5\,b^3-17\,B^2\,C\,a^4\,b^4+9\,B^2\,C\,a^3\,b^5+11\,B^2\,C\,a^2\,b^6-12\,B\,C^2\,a^7\,b+8\,B\,C^2\,a^6\,b^2+32\,B\,C^2\,a^5\,b^3-13\,B\,C^2\,a^4\,b^4-20\,B\,C^2\,a^3\,b^5+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}\right)}{b^3}+\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{\left(B\,b-2\,C\,a\right)\,\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-2\,C\,a\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}\right)}{b^3}}\right)\,\left(B\,b-2\,C\,a\right)\,2{}\mathrm{i}}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(-A^2\,B\,b^8+2\,A^2\,C\,a\,b^7-A\,B^2\,a^3\,b^5-A\,B^2\,a^2\,b^6+3\,A\,B^2\,a\,b^7+A\,B^2\,b^8+4\,A\,B\,C\,a^4\,b^4+4\,A\,B\,C\,a^3\,b^5-10\,A\,B\,C\,a^2\,b^6-4\,A\,B\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6-B^3\,a^5\,b^3+B^3\,a^4\,b^4+3\,B^3\,a^3\,b^5-2\,B^3\,a^2\,b^6-2\,B^3\,a\,b^7+6\,B^2\,C\,a^6\,b^2-5\,B^2\,C\,a^5\,b^3-17\,B^2\,C\,a^4\,b^4+9\,B^2\,C\,a^3\,b^5+11\,B^2\,C\,a^2\,b^6-12\,B\,C^2\,a^7\,b+8\,B\,C^2\,a^6\,b^2+32\,B\,C^2\,a^5\,b^3-13\,B\,C^2\,a^4\,b^4-20\,B\,C^2\,a^3\,b^5+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}-\frac{\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)*(2*C*a^3 - C*b^3 + A*a*b^2 - B*a^2*b - C*a*b^2 + C*a^2*b))/(b^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)^3*(2*C*a^3 + C*b^3 + A*a*b^2 - B*a^2*b - C*a*b^2 - C*a^2*b))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) - 2*a*tan(c/2 + (d*x)/2)^2)) - (atan((((B*b - 2*C*a)*(((B*b - 2*C*a)*((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3 - (32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))*1i)/b^3 - ((B*b - 2*C*a)*(((B*b - 2*C*a)*((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3 + (32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))*1i)/b^3)/((64*(8*C^3*a^8 + A*B^2*b^8 - A^2*B*b^8 - 2*B^3*a*b^7 - 4*C^3*a^7*b - 2*B^3*a^2*b^6 + 3*B^3*a^3*b^5 + B^3*a^4*b^4 - B^3*a^5*b^3 + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 3*A*B^2*a*b^7 + 2*A^2*C*a*b^7 - 12*B*C^2*a^7*b - A*B^2*a^2*b^6 - A*B^2*a^3*b^5 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3 - 20*B*C^2*a^3*b^5 - 13*B*C^2*a^4*b^4 + 32*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 11*B^2*C*a^2*b^6 + 9*B^2*C*a^3*b^5 - 17*B^2*C*a^4*b^4 - 5*B^2*C*a^5*b^3 + 6*B^2*C*a^6*b^2 - 4*A*B*C*a*b^7 - 10*A*B*C*a^2*b^6 + 4*A*B*C*a^3*b^5 + 4*A*B*C*a^4*b^4))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + ((B*b - 2*C*a)*(((B*b - 2*C*a)*((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3 - (32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))/b^3 + ((B*b - 2*C*a)*(((B*b - 2*C*a)*((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(B*b - 2*C*a)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3 + (32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))/b^3))*(B*b - 2*C*a)*2i)/(b^3*d) + (atan(((((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*C^3*a^8 + A*B^2*b^8 - A^2*B*b^8 - 2*B^3*a*b^7 - 4*C^3*a^7*b - 2*B^3*a^2*b^6 + 3*B^3*a^3*b^5 + B^3*a^4*b^4 - B^3*a^5*b^3 + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 3*A*B^2*a*b^7 + 2*A^2*C*a*b^7 - 12*B*C^2*a^7*b - A*B^2*a^2*b^6 - A*B^2*a^3*b^5 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3 - 20*B*C^2*a^3*b^5 - 13*B*C^2*a^4*b^4 + 32*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 11*B^2*C*a^2*b^6 + 9*B^2*C*a^3*b^5 - 17*B^2*C*a^4*b^4 - 5*B^2*C*a^5*b^3 + 6*B^2*C*a^6*b^2 - 4*A*B*C*a*b^7 - 10*A*B*C*a^2*b^6 + 4*A*B*C*a^3*b^5 + 4*A*B*C*a^4*b^4))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) - (((a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
911,1,4536,148,13.125212,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^2),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}\right)\,1{}\mathrm{i}}{b^2}+\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}\right)\,1{}\mathrm{i}}{b^2}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-2\,A\,B\,C\,a\,b^4-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}\right)}{b^2}+\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)}{b^2}\right)}{b^2}}\right)\,2{}\mathrm{i}}{b^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-2\,A\,B\,C\,a\,b^4-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"- (C*atan(((C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2)*1i)/b^2 + (C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2)*1i)/b^2)/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b - 3*B*C^2*a*b^4 + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2 - 2*A*B*C*a*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2))/b^2 + (C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))))/b^2))/b^2))*2i)/(b^2*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b - 3*B*C^2*a*b^4 + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2 - 2*A*B*C*a*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 - B*a*b))/(d*(a + b)*(a*b - b^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
912,1,4544,138,13.316656,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^2,x)","\frac{2\,A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)}{a^2}+\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)}{a^2}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5-A^2\,B\,a^5-3\,A^2\,B\,a^4\,b+A^2\,B\,a^3\,b^2+A^2\,B\,a^2\,b^3+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,B^2\,a^5-2\,A\,B\,C\,a^4\,b+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}-\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5-A^2\,B\,a^5-3\,A^2\,B\,a^4\,b+A^2\,B\,a^3\,b^2+A^2\,B\,a^2\,b^3+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,B^2\,a^5-2\,A\,B\,C\,a^4\,b+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"(2*A*atan(((A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2))/a^2 + (A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2))/a^2)/((64*(A^3*b^5 + A*B^2*a^5 - A^2*B*a^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - 3*A^2*B*a^4*b - A^2*C*a*b^4 + A^2*C*a^4*b + A^2*B*a^2*b^3 + A^2*B*a^3*b^2 + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2 - 2*A*B*C*a^4*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2)*1i)/a^2 - (A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/a^2)*1i)/a^2)))/(a^2*d) + (atan(((((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(A^3*b^5 + A*B^2*a^5 - A^2*B*a^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - 3*A^2*B*a^4*b - A^2*C*a*b^4 + A^2*C*a^4*b + A^2*B*a^2*b^3 + A^2*B*a^3*b^2 + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2 - 2*A*B*C*a^4*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) - (((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 - B*a*b))/(d*(a + b)*(a*b - a^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
913,1,3804,202,9.851482,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^3-2\,A\,b^3-A\,a\,b^2+A\,a^2\,b+B\,a\,b^2-C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^3+2\,A\,b^3-A\,a\,b^2-A\,a^2\,b-B\,a\,b^2+C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(2\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(A\,b\,2{}\mathrm{i}-B\,a\,1{}\mathrm{i}\right)}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8-20\,A^2\,B\,a^5\,b^3-13\,A^2\,B\,a^4\,b^4+32\,A^2\,B\,a^3\,b^5+8\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+11\,A\,B^2\,a^6\,b^2+9\,A\,B^2\,a^5\,b^3-17\,A\,B^2\,a^4\,b^4-5\,A\,B^2\,a^3\,b^5+6\,A\,B^2\,a^2\,b^6-4\,A\,B\,C\,a^7\,b-10\,A\,B\,C\,a^6\,b^2+4\,A\,B\,C\,a^5\,b^3+4\,A\,B\,C\,a^4\,b^4+2\,A\,C^2\,a^7\,b-2\,B^3\,a^7\,b-2\,B^3\,a^6\,b^2+3\,B^3\,a^5\,b^3+B^3\,a^4\,b^4-B^3\,a^3\,b^5+B^2\,C\,a^8+3\,B^2\,C\,a^7\,b-B^2\,C\,a^6\,b^2-B^2\,C\,a^5\,b^3-B\,C^2\,a^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)*(A*a^3 - 2*A*b^3 - A*a*b^2 + A*a^2*b + B*a*b^2 - C*a^2*b))/(a^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)^3*(A*a^3 + 2*A*b^3 - A*a*b^2 - A*a^2*b - B*a*b^2 + C*a^2*b))/(a^2*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) + 2*b*tan(c/2 + (d*x)/2)^2)) + (log(tan(c/2 + (d*x)/2) - 1i)*(2*A*b - B*a)*1i)/(a^3*d) - (log(tan(c/2 + (d*x)/2) + 1i)*(A*b*2i - B*a*1i))/(a^3*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*A^3*b^8 - B*C^2*a^8 + B^2*C*a^8 - 4*A^3*a*b^7 - 2*B^3*a^7*b - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 - B^3*a^3*b^5 + B^3*a^4*b^4 + 3*B^3*a^5*b^3 - 2*B^3*a^6*b^2 - 12*A^2*B*a*b^7 + 2*A*C^2*a^7*b + 3*B^2*C*a^7*b + 6*A*B^2*a^2*b^6 - 5*A*B^2*a^3*b^5 - 17*A*B^2*a^4*b^4 + 9*A*B^2*a^5*b^3 + 11*A*B^2*a^6*b^2 + 8*A^2*B*a^2*b^6 + 32*A^2*B*a^3*b^5 - 13*A^2*B*a^4*b^4 - 20*A^2*B*a^5*b^3 - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2 - B^2*C*a^5*b^3 - B^2*C*a^6*b^2 - 4*A*B*C*a^7*b + 4*A*B*C*a^4*b^4 + 4*A*B*C*a^5*b^3 - 10*A*B*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
914,1,9997,298,15.972656,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^4+6\,A\,b^4+2\,B\,a^4-5\,A\,a^2\,b^2-2\,B\,a^2\,b^2+2\,C\,a^2\,b^2+3\,A\,a\,b^3-3\,A\,a^3\,b-4\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A\,a^4+6\,A\,b^4-2\,B\,a^4-5\,A\,a^2\,b^2+2\,B\,a^2\,b^2+2\,C\,a^2\,b^2-3\,A\,a\,b^3+3\,A\,a^3\,b-4\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^4-6\,A\,b^4+3\,A\,a^2\,b^2-2\,C\,a^2\,b^2+4\,B\,a\,b^3-2\,B\,a^3\,b\right)}{a\,\left(a^2\,b-a^3\right)\,\left(a+b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(a+3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^4}}{-\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}-3\,A^2\,B\,a^9\,b^2+3\,A^2\,B\,a^8\,b^3-63\,A^2\,B\,a^7\,b^4+15\,A^2\,B\,a^6\,b^5-186\,A^2\,B\,a^5\,b^6-162\,A^2\,B\,a^4\,b^7+468\,A^2\,B\,a^3\,b^8+108\,A^2\,B\,a^2\,b^9-216\,A^2\,B\,a\,b^{10}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+24\,A\,B^2\,a^8\,b^3-6\,A\,B^2\,a^7\,b^4+168\,A\,B^2\,a^6\,b^5+108\,A\,B^2\,a^5\,b^6-336\,A\,B^2\,a^4\,b^7-72\,A\,B^2\,a^3\,b^8+144\,A\,B^2\,a^2\,b^9-28\,A\,B\,C\,a^9\,b^2+4\,A\,B\,C\,a^8\,b^3-188\,A\,B\,C\,a^7\,b^4-152\,A\,B\,C\,a^6\,b^5+360\,A\,B\,C\,a^5\,b^6+96\,A\,B\,C\,a^4\,b^7-144\,A\,B\,C\,a^3\,b^8+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7-48\,B^3\,a^7\,b^4-24\,B^3\,a^6\,b^5+80\,B^3\,a^5\,b^6+16\,B^3\,a^4\,b^7-32\,B^3\,a^3\,b^8+80\,B^2\,C\,a^8\,b^3+52\,B^2\,C\,a^7\,b^4-128\,B^2\,C\,a^6\,b^5-32\,B^2\,C\,a^5\,b^6+48\,B^2\,C\,a^4\,b^7-44\,B\,C^2\,a^9\,b^2-36\,B\,C^2\,a^8\,b^3+68\,B\,C^2\,a^7\,b^4+20\,B\,C^2\,a^6\,b^5-24\,B\,C^2\,a^5\,b^6+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)}{a^4}+\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)}{a^4}}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-2{}\mathrm{i}\,B\,a\,b+3{}\mathrm{i}\,A\,b^2\right)\,2{}\mathrm{i}}{a^4\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}-3\,A^2\,B\,a^9\,b^2+3\,A^2\,B\,a^8\,b^3-63\,A^2\,B\,a^7\,b^4+15\,A^2\,B\,a^6\,b^5-186\,A^2\,B\,a^5\,b^6-162\,A^2\,B\,a^4\,b^7+468\,A^2\,B\,a^3\,b^8+108\,A^2\,B\,a^2\,b^9-216\,A^2\,B\,a\,b^{10}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+24\,A\,B^2\,a^8\,b^3-6\,A\,B^2\,a^7\,b^4+168\,A\,B^2\,a^6\,b^5+108\,A\,B^2\,a^5\,b^6-336\,A\,B^2\,a^4\,b^7-72\,A\,B^2\,a^3\,b^8+144\,A\,B^2\,a^2\,b^9-28\,A\,B\,C\,a^9\,b^2+4\,A\,B\,C\,a^8\,b^3-188\,A\,B\,C\,a^7\,b^4-152\,A\,B\,C\,a^6\,b^5+360\,A\,B\,C\,a^5\,b^6+96\,A\,B\,C\,a^4\,b^7-144\,A\,B\,C\,a^3\,b^8+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7-48\,B^3\,a^7\,b^4-24\,B^3\,a^6\,b^5+80\,B^3\,a^5\,b^6+16\,B^3\,a^4\,b^7-32\,B^3\,a^3\,b^8+80\,B^2\,C\,a^8\,b^3+52\,B^2\,C\,a^7\,b^4-128\,B^2\,C\,a^6\,b^5-32\,B^2\,C\,a^5\,b^6+48\,B^2\,C\,a^4\,b^7-44\,B\,C^2\,a^9\,b^2-36\,B\,C^2\,a^8\,b^3+68\,B\,C^2\,a^7\,b^4+20\,B\,C^2\,a^6\,b^5-24\,B\,C^2\,a^5\,b^6+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"(atan(-((((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i))/a^4 + (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*1i)/a^4 - (((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i))/a^4 - (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*1i)/a^4)/((((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i))/a^4 + (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i))/a^4 - (16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 - 32*B^3*a^3*b^8 + 16*B^3*a^4*b^7 + 80*B^3*a^5*b^6 - 24*B^3*a^6*b^5 - 48*B^3*a^7*b^4 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 - 216*A^2*B*a*b^10 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 144*A*B^2*a^2*b^9 - 72*A*B^2*a^3*b^8 - 336*A*B^2*a^4*b^7 + 108*A*B^2*a^5*b^6 + 168*A*B^2*a^6*b^5 - 6*A*B^2*a^7*b^4 + 24*A*B^2*a^8*b^3 + 108*A^2*B*a^2*b^9 + 468*A^2*B*a^3*b^8 - 162*A^2*B*a^4*b^7 - 186*A^2*B*a^5*b^6 + 15*A^2*B*a^6*b^5 - 63*A^2*B*a^7*b^4 + 3*A^2*B*a^8*b^3 - 3*A^2*B*a^9*b^2 + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2 - 24*B*C^2*a^5*b^6 + 20*B*C^2*a^6*b^5 + 68*B*C^2*a^7*b^4 - 36*B*C^2*a^8*b^3 - 44*B*C^2*a^9*b^2 + 48*B^2*C*a^4*b^7 - 32*B^2*C*a^5*b^6 - 128*B^2*C*a^6*b^5 + 52*B^2*C*a^7*b^4 + 80*B^2*C*a^8*b^3 - 144*A*B*C*a^3*b^8 + 96*A*B*C*a^4*b^7 + 360*A*B*C*a^5*b^6 - 152*A*B*C*a^6*b^5 - 188*A*B*C*a^7*b^4 + 4*A*B*C*a^8*b^3 - 28*A*B*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i))/a^4 - (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i))/a^4))*(A*b^2*3i + a^2*((A*1i)/2 + C*1i) - B*a*b*2i)*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)*(A*a^4 + 6*A*b^4 + 2*B*a^4 - 5*A*a^2*b^2 - 2*B*a^2*b^2 + 2*C*a^2*b^2 + 3*A*a*b^3 - 3*A*a^3*b - 4*B*a*b^3 + 2*B*a^3*b))/((a^3*b - a^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(A*a^4 + 6*A*b^4 - 2*B*a^4 - 5*A*a^2*b^2 + 2*B*a^2*b^2 + 2*C*a^2*b^2 - 3*A*a*b^3 + 3*A*a^3*b - 4*B*a*b^3 + 2*B*a^3*b))/((a^3*b - a^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(A*a^4 - 6*A*b^4 + 3*A*a^2*b^2 - 2*C*a^2*b^2 + 4*B*a*b^3 - 2*B*a^3*b))/(a*(a^2*b - a^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) - tan(c/2 + (d*x)/2)^6*(a - b))) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 - 32*B^3*a^3*b^8 + 16*B^3*a^4*b^7 + 80*B^3*a^5*b^6 - 24*B^3*a^6*b^5 - 48*B^3*a^7*b^4 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 - 216*A^2*B*a*b^10 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 144*A*B^2*a^2*b^9 - 72*A*B^2*a^3*b^8 - 336*A*B^2*a^4*b^7 + 108*A*B^2*a^5*b^6 + 168*A*B^2*a^6*b^5 - 6*A*B^2*a^7*b^4 + 24*A*B^2*a^8*b^3 + 108*A^2*B*a^2*b^9 + 468*A^2*B*a^3*b^8 - 162*A^2*B*a^4*b^7 - 186*A^2*B*a^5*b^6 + 15*A^2*B*a^6*b^5 - 63*A^2*B*a^7*b^4 + 3*A^2*B*a^8*b^3 - 3*A^2*B*a^9*b^2 + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2 - 24*B*C^2*a^5*b^6 + 20*B*C^2*a^6*b^5 + 68*B*C^2*a^7*b^4 - 36*B*C^2*a^8*b^3 - 44*B*C^2*a^9*b^2 + 48*B^2*C*a^4*b^7 - 32*B^2*C*a^5*b^6 - 128*B^2*C*a^6*b^5 + 52*B^2*C*a^7*b^4 + 80*B^2*C*a^8*b^3 - 144*A*B*C*a^3*b^8 + 96*A*B*C*a^4*b^7 + 360*A*B*C*a^5*b^6 - 152*A*B*C*a^6*b^5 - 188*A*B*C*a^7*b^4 + 4*A*B*C*a^8*b^3 - 28*A*B*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
915,1,11743,396,17.678384,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^5-8\,A\,b^5+B\,a^5+2\,C\,a^5+6\,A\,a^2\,b^3+2\,A\,a^3\,b^2+3\,B\,a^2\,b^3-5\,B\,a^3\,b^2-4\,C\,a^2\,b^3-2\,C\,a^3\,b^2-4\,A\,a\,b^4+6\,B\,a\,b^4-3\,B\,a^4\,b+2\,C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^5+72\,A\,b^5+3\,B\,a^5-6\,C\,a^5-38\,A\,a^2\,b^3-14\,A\,a^3\,b^2-9\,B\,a^2\,b^3+33\,B\,a^3\,b^2+36\,C\,a^2\,b^3+6\,C\,a^3\,b^2+12\,A\,a\,b^4-16\,A\,a^4\,b-54\,B\,a\,b^4+9\,B\,a^4\,b-18\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^5-72\,A\,b^5-3\,B\,a^5-6\,C\,a^5+38\,A\,a^2\,b^3-14\,A\,a^3\,b^2-9\,B\,a^2\,b^3-33\,B\,a^3\,b^2-36\,C\,a^2\,b^3+6\,C\,a^3\,b^2+12\,A\,a\,b^4+16\,A\,a^4\,b+54\,B\,a\,b^4+9\,B\,a^4\,b+18\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^5+8\,A\,b^5-B\,a^5+2\,C\,a^5-6\,A\,a^2\,b^3+2\,A\,a^3\,b^2+3\,B\,a^2\,b^3+5\,B\,a^3\,b^2+4\,C\,a^2\,b^3-2\,C\,a^3\,b^2-4\,A\,a\,b^4-6\,B\,a\,b^4-3\,B\,a^4\,b-2\,C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,b-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(2\,a+4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^5}}{\frac{16\,\left(20\,A^3\,a^8\,b^6-20\,A^3\,a^7\,b^7+124\,A^3\,a^6\,b^8-24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}+192\,A^3\,a^3\,b^{11}-448\,A^3\,a^2\,b^{12}-128\,A^3\,a\,b^{13}+256\,A^3\,b^{14}-36\,A^2\,B\,a^9\,b^5+36\,A^2\,B\,a^8\,b^6-264\,A^2\,B\,a^7\,b^7+54\,A^2\,B\,a^6\,b^8-180\,A^2\,B\,a^5\,b^9-432\,A^2\,B\,a^4\,b^{10}+1056\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-576\,A^2\,B\,a\,b^{13}+12\,A^2\,C\,a^{10}\,b^4-12\,A^2\,C\,a^9\,b^5+156\,A^2\,C\,a^8\,b^6-36\,A^2\,C\,a^7\,b^7+216\,A^2\,C\,a^6\,b^8+288\,A^2\,C\,a^5\,b^9-768\,A^2\,C\,a^4\,b^{10}-192\,A^2\,C\,a^3\,b^{11}+384\,A^2\,C\,a^2\,b^{12}+21\,A\,B^2\,a^{10}\,b^4-21\,A\,B^2\,a^9\,b^5+183\,A\,B^2\,a^8\,b^6-39\,A\,B^2\,a^7\,b^7+192\,A\,B^2\,a^6\,b^8+324\,A\,B^2\,a^5\,b^9-828\,A\,B^2\,a^4\,b^{10}-216\,A\,B^2\,a^3\,b^{11}+432\,A\,B^2\,a^2\,b^{12}-12\,A\,B\,C\,a^{11}\,b^3+12\,A\,B\,C\,a^{10}\,b^4-204\,A\,B\,C\,a^9\,b^5+48\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7-432\,A\,B\,C\,a^6\,b^8+1200\,A\,B\,C\,a^5\,b^9+288\,A\,B\,C\,a^4\,b^{10}-576\,A\,B\,C\,a^3\,b^{11}+48\,A\,C^2\,a^{10}\,b^4-12\,A\,C^2\,a^9\,b^5+192\,A\,C^2\,a^8\,b^6+144\,A\,C^2\,a^7\,b^7-432\,A\,C^2\,a^6\,b^8-96\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}-4\,B^3\,a^{11}\,b^3+4\,B^3\,a^{10}\,b^4-41\,B^3\,a^9\,b^5+9\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7-81\,B^3\,a^6\,b^8+216\,B^3\,a^5\,b^9+54\,B^3\,a^4\,b^{10}-108\,B^3\,a^3\,b^{11}+3\,B^2\,C\,a^{12}\,b^2-3\,B^2\,C\,a^{11}\,b^3+63\,B^2\,C\,a^{10}\,b^4-15\,B^2\,C\,a^9\,b^5+186\,B^2\,C\,a^8\,b^6+162\,B^2\,C\,a^7\,b^7-468\,B^2\,C\,a^6\,b^8-108\,B^2\,C\,a^5\,b^9+216\,B^2\,C\,a^4\,b^{10}-24\,B\,C^2\,a^{11}\,b^3+6\,B\,C^2\,a^{10}\,b^4-168\,B\,C^2\,a^9\,b^5-108\,B\,C^2\,a^8\,b^6+336\,B\,C^2\,a^7\,b^7+72\,B\,C^2\,a^6\,b^8-144\,B\,C^2\,a^5\,b^9+48\,C^3\,a^{10}\,b^4+24\,C^3\,a^9\,b^5-80\,C^3\,a^8\,b^6-16\,C^3\,a^7\,b^7+32\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)}{a^5}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)}{a^5}}\right)\,\left(A\,b^3\,4{}\mathrm{i}-\frac{B\,a^3\,1{}\mathrm{i}}{2}+a^2\,\left(A\,b\,1{}\mathrm{i}+C\,b\,2{}\mathrm{i}\right)-B\,a\,b^2\,3{}\mathrm{i}\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}{\frac{16\,\left(20\,A^3\,a^8\,b^6-20\,A^3\,a^7\,b^7+124\,A^3\,a^6\,b^8-24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}+192\,A^3\,a^3\,b^{11}-448\,A^3\,a^2\,b^{12}-128\,A^3\,a\,b^{13}+256\,A^3\,b^{14}-36\,A^2\,B\,a^9\,b^5+36\,A^2\,B\,a^8\,b^6-264\,A^2\,B\,a^7\,b^7+54\,A^2\,B\,a^6\,b^8-180\,A^2\,B\,a^5\,b^9-432\,A^2\,B\,a^4\,b^{10}+1056\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-576\,A^2\,B\,a\,b^{13}+12\,A^2\,C\,a^{10}\,b^4-12\,A^2\,C\,a^9\,b^5+156\,A^2\,C\,a^8\,b^6-36\,A^2\,C\,a^7\,b^7+216\,A^2\,C\,a^6\,b^8+288\,A^2\,C\,a^5\,b^9-768\,A^2\,C\,a^4\,b^{10}-192\,A^2\,C\,a^3\,b^{11}+384\,A^2\,C\,a^2\,b^{12}+21\,A\,B^2\,a^{10}\,b^4-21\,A\,B^2\,a^9\,b^5+183\,A\,B^2\,a^8\,b^6-39\,A\,B^2\,a^7\,b^7+192\,A\,B^2\,a^6\,b^8+324\,A\,B^2\,a^5\,b^9-828\,A\,B^2\,a^4\,b^{10}-216\,A\,B^2\,a^3\,b^{11}+432\,A\,B^2\,a^2\,b^{12}-12\,A\,B\,C\,a^{11}\,b^3+12\,A\,B\,C\,a^{10}\,b^4-204\,A\,B\,C\,a^9\,b^5+48\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7-432\,A\,B\,C\,a^6\,b^8+1200\,A\,B\,C\,a^5\,b^9+288\,A\,B\,C\,a^4\,b^{10}-576\,A\,B\,C\,a^3\,b^{11}+48\,A\,C^2\,a^{10}\,b^4-12\,A\,C^2\,a^9\,b^5+192\,A\,C^2\,a^8\,b^6+144\,A\,C^2\,a^7\,b^7-432\,A\,C^2\,a^6\,b^8-96\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}-4\,B^3\,a^{11}\,b^3+4\,B^3\,a^{10}\,b^4-41\,B^3\,a^9\,b^5+9\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7-81\,B^3\,a^6\,b^8+216\,B^3\,a^5\,b^9+54\,B^3\,a^4\,b^{10}-108\,B^3\,a^3\,b^{11}+3\,B^2\,C\,a^{12}\,b^2-3\,B^2\,C\,a^{11}\,b^3+63\,B^2\,C\,a^{10}\,b^4-15\,B^2\,C\,a^9\,b^5+186\,B^2\,C\,a^8\,b^6+162\,B^2\,C\,a^7\,b^7-468\,B^2\,C\,a^6\,b^8-108\,B^2\,C\,a^5\,b^9+216\,B^2\,C\,a^4\,b^{10}-24\,B\,C^2\,a^{11}\,b^3+6\,B\,C^2\,a^{10}\,b^4-168\,B\,C^2\,a^9\,b^5-108\,B\,C^2\,a^8\,b^6+336\,B\,C^2\,a^7\,b^7+72\,B\,C^2\,a^6\,b^8-144\,B\,C^2\,a^5\,b^9+48\,C^3\,a^{10}\,b^4+24\,C^3\,a^9\,b^5-80\,C^3\,a^8\,b^6-16\,C^3\,a^7\,b^7+32\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}-\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^5 - 8*A*b^5 + B*a^5 + 2*C*a^5 + 6*A*a^2*b^3 + 2*A*a^3*b^2 + 3*B*a^2*b^3 - 5*B*a^3*b^2 - 4*C*a^2*b^3 - 2*C*a^3*b^2 - 4*A*a*b^4 + 6*B*a*b^4 - 3*B*a^4*b + 2*C*a^4*b))/(a^4*(a + b)*(a - b)) - (tan(c/2 + (d*x)/2)^3*(2*A*a^5 + 72*A*b^5 + 3*B*a^5 - 6*C*a^5 - 38*A*a^2*b^3 - 14*A*a^3*b^2 - 9*B*a^2*b^3 + 33*B*a^3*b^2 + 36*C*a^2*b^3 + 6*C*a^3*b^2 + 12*A*a*b^4 - 16*A*a^4*b - 54*B*a*b^4 + 9*B*a^4*b - 18*C*a^4*b))/(3*a^4*(a + b)*(a - b)) + (tan(c/2 + (d*x)/2)^5*(2*A*a^5 - 72*A*b^5 - 3*B*a^5 - 6*C*a^5 + 38*A*a^2*b^3 - 14*A*a^3*b^2 - 9*B*a^2*b^3 - 33*B*a^3*b^2 - 36*C*a^2*b^3 + 6*C*a^3*b^2 + 12*A*a*b^4 + 16*A*a^4*b + 54*B*a*b^4 + 9*B*a^4*b + 18*C*a^4*b))/(3*a^4*(a + b)*(a - b)) - (tan(c/2 + (d*x)/2)^7*(2*A*a^5 + 8*A*b^5 - B*a^5 + 2*C*a^5 - 6*A*a^2*b^3 + 2*A*a^3*b^2 + 3*B*a^2*b^3 + 5*B*a^3*b^2 + 4*C*a^2*b^3 - 2*C*a^3*b^2 - 4*A*a*b^4 - 6*B*a*b^4 - 3*B*a^4*b - 2*C*a^4*b))/(a^4*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^8*(a - b) + tan(c/2 + (d*x)/2)^2*(2*a + 4*b) - tan(c/2 + (d*x)/2)^6*(2*a - 4*b) + 6*b*tan(c/2 + (d*x)/2)^4)) - (atan(((((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i))/a^5 + (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*1i)/a^5 - (((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i))/a^5 - (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*1i)/a^5)/((16*(256*A^3*b^14 - 128*A^3*a*b^13 - 448*A^3*a^2*b^12 + 192*A^3*a^3*b^11 + 48*A^3*a^4*b^10 - 24*A^3*a^5*b^9 + 124*A^3*a^6*b^8 - 20*A^3*a^7*b^7 + 20*A^3*a^8*b^6 - 108*B^3*a^3*b^11 + 54*B^3*a^4*b^10 + 216*B^3*a^5*b^9 - 81*B^3*a^6*b^8 - 63*B^3*a^7*b^7 + 9*B^3*a^8*b^6 - 41*B^3*a^9*b^5 + 4*B^3*a^10*b^4 - 4*B^3*a^11*b^3 + 32*C^3*a^6*b^8 - 16*C^3*a^7*b^7 - 80*C^3*a^8*b^6 + 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 - 576*A^2*B*a*b^13 + 432*A*B^2*a^2*b^12 - 216*A*B^2*a^3*b^11 - 828*A*B^2*a^4*b^10 + 324*A*B^2*a^5*b^9 + 192*A*B^2*a^6*b^8 - 39*A*B^2*a^7*b^7 + 183*A*B^2*a^8*b^6 - 21*A*B^2*a^9*b^5 + 21*A*B^2*a^10*b^4 + 288*A^2*B*a^2*b^12 + 1056*A^2*B*a^3*b^11 - 432*A^2*B*a^4*b^10 - 180*A^2*B*a^5*b^9 + 54*A^2*B*a^6*b^8 - 264*A^2*B*a^7*b^7 + 36*A^2*B*a^8*b^6 - 36*A^2*B*a^9*b^5 + 192*A*C^2*a^4*b^10 - 96*A*C^2*a^5*b^9 - 432*A*C^2*a^6*b^8 + 144*A*C^2*a^7*b^7 + 192*A*C^2*a^8*b^6 - 12*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 + 384*A^2*C*a^2*b^12 - 192*A^2*C*a^3*b^11 - 768*A^2*C*a^4*b^10 + 288*A^2*C*a^5*b^9 + 216*A^2*C*a^6*b^8 - 36*A^2*C*a^7*b^7 + 156*A^2*C*a^8*b^6 - 12*A^2*C*a^9*b^5 + 12*A^2*C*a^10*b^4 - 144*B*C^2*a^5*b^9 + 72*B*C^2*a^6*b^8 + 336*B*C^2*a^7*b^7 - 108*B*C^2*a^8*b^6 - 168*B*C^2*a^9*b^5 + 6*B*C^2*a^10*b^4 - 24*B*C^2*a^11*b^3 + 216*B^2*C*a^4*b^10 - 108*B^2*C*a^5*b^9 - 468*B^2*C*a^6*b^8 + 162*B^2*C*a^7*b^7 + 186*B^2*C*a^8*b^6 - 15*B^2*C*a^9*b^5 + 63*B^2*C*a^10*b^4 - 3*B^2*C*a^11*b^3 + 3*B^2*C*a^12*b^2 - 576*A*B*C*a^3*b^11 + 288*A*B*C*a^4*b^10 + 1200*A*B*C*a^5*b^9 - 432*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 + 48*A*B*C*a^8*b^6 - 204*A*B*C*a^9*b^5 + 12*A*B*C*a^10*b^4 - 12*A*B*C*a^11*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i))/a^5 + (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i))/a^5 + (((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i))/a^5 - (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i))/a^5))*(A*b^3*4i - (B*a^3*1i)/2 + a^2*(A*b*1i + C*b*2i) - B*a*b^2*3i)*2i)/(a^5*d) - (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))/((16*(256*A^3*b^14 - 128*A^3*a*b^13 - 448*A^3*a^2*b^12 + 192*A^3*a^3*b^11 + 48*A^3*a^4*b^10 - 24*A^3*a^5*b^9 + 124*A^3*a^6*b^8 - 20*A^3*a^7*b^7 + 20*A^3*a^8*b^6 - 108*B^3*a^3*b^11 + 54*B^3*a^4*b^10 + 216*B^3*a^5*b^9 - 81*B^3*a^6*b^8 - 63*B^3*a^7*b^7 + 9*B^3*a^8*b^6 - 41*B^3*a^9*b^5 + 4*B^3*a^10*b^4 - 4*B^3*a^11*b^3 + 32*C^3*a^6*b^8 - 16*C^3*a^7*b^7 - 80*C^3*a^8*b^6 + 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 - 576*A^2*B*a*b^13 + 432*A*B^2*a^2*b^12 - 216*A*B^2*a^3*b^11 - 828*A*B^2*a^4*b^10 + 324*A*B^2*a^5*b^9 + 192*A*B^2*a^6*b^8 - 39*A*B^2*a^7*b^7 + 183*A*B^2*a^8*b^6 - 21*A*B^2*a^9*b^5 + 21*A*B^2*a^10*b^4 + 288*A^2*B*a^2*b^12 + 1056*A^2*B*a^3*b^11 - 432*A^2*B*a^4*b^10 - 180*A^2*B*a^5*b^9 + 54*A^2*B*a^6*b^8 - 264*A^2*B*a^7*b^7 + 36*A^2*B*a^8*b^6 - 36*A^2*B*a^9*b^5 + 192*A*C^2*a^4*b^10 - 96*A*C^2*a^5*b^9 - 432*A*C^2*a^6*b^8 + 144*A*C^2*a^7*b^7 + 192*A*C^2*a^8*b^6 - 12*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 + 384*A^2*C*a^2*b^12 - 192*A^2*C*a^3*b^11 - 768*A^2*C*a^4*b^10 + 288*A^2*C*a^5*b^9 + 216*A^2*C*a^6*b^8 - 36*A^2*C*a^7*b^7 + 156*A^2*C*a^8*b^6 - 12*A^2*C*a^9*b^5 + 12*A^2*C*a^10*b^4 - 144*B*C^2*a^5*b^9 + 72*B*C^2*a^6*b^8 + 336*B*C^2*a^7*b^7 - 108*B*C^2*a^8*b^6 - 168*B*C^2*a^9*b^5 + 6*B*C^2*a^10*b^4 - 24*B*C^2*a^11*b^3 + 216*B^2*C*a^4*b^10 - 108*B^2*C*a^5*b^9 - 468*B^2*C*a^6*b^8 + 162*B^2*C*a^7*b^7 + 186*B^2*C*a^8*b^6 - 15*B^2*C*a^9*b^5 + 63*B^2*C*a^10*b^4 - 3*B^2*C*a^11*b^3 + 3*B^2*C*a^12*b^2 - 576*A*B*C*a^3*b^11 + 288*A*B*C*a^4*b^10 + 1200*A*B*C*a^5*b^9 - 432*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 + 48*A*B*C*a^8*b^6 - 204*A*B*C*a^9*b^5 + 12*A*B*C*a^10*b^4 - 12*A*B*C*a^11*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) - (b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b)*2i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
916,1,15937,465,21.043993,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b/cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b^7+36\,C\,a^7+3\,C\,b^7-6\,A\,a^2\,b^5-15\,A\,a^3\,b^4+3\,A\,a^4\,b^3+6\,A\,a^5\,b^2-10\,B\,a^2\,b^5+16\,B\,a^3\,b^4+35\,B\,a^4\,b^3-9\,B\,a^5\,b^2+5\,C\,a^2\,b^5+26\,C\,a^3\,b^4-29\,C\,a^4\,b^3-67\,C\,a^5\,b^2-4\,B\,a\,b^6-18\,B\,a^6\,b-4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,C\,b^7-36\,C\,a^7-2\,B\,b^7-6\,A\,a^2\,b^5+15\,A\,a^3\,b^4+3\,A\,a^4\,b^3-6\,A\,a^5\,b^2+10\,B\,a^2\,b^5+16\,B\,a^3\,b^4-35\,B\,a^4\,b^3-9\,B\,a^5\,b^2+5\,C\,a^2\,b^5-26\,C\,a^3\,b^4-29\,C\,a^4\,b^3+67\,C\,a^5\,b^2-4\,B\,a\,b^6+18\,B\,a^6\,b+4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(C\,b^6-12\,C\,a^6-2\,B\,b^6+6\,A\,a^2\,b^4+A\,a^3\,b^3-2\,A\,a^4\,b^2+4\,B\,a^2\,b^4-12\,B\,a^3\,b^3-3\,B\,a^4\,b^2-8\,C\,a^2\,b^4-10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+2\,B\,a\,b^5+6\,B\,a^5\,b+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a\,b^4-b^5\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^6-12\,C\,a^6+C\,b^6+6\,A\,a^2\,b^4-A\,a^3\,b^3-2\,A\,a^4\,b^2-4\,B\,a^2\,b^4-12\,B\,a^3\,b^3+3\,B\,a^4\,b^2-8\,C\,a^2\,b^4+10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+2\,B\,a\,b^5+6\,B\,a^5\,b-5\,C\,a\,b^5-6\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b\,a\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2-3\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,C\,a^2-3\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)\,\left(6\,C\,a^2-3\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(\frac{\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^2-3\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,C\,a^2-3\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)\,\left(6\,C\,a^2-3\,B\,a\,b+\left(A+\frac{C}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^5}}{\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}-72\,A^2\,B\,a^{10}\,b^5+36\,A^2\,B\,a^9\,b^6+324\,A^2\,B\,a^8\,b^7-210\,A^2\,B\,a^7\,b^8-624\,A^2\,B\,a^6\,b^9+396\,A^2\,B\,a^5\,b^{10}+564\,A^2\,B\,a^4\,b^{11}-312\,A^2\,B\,a^3\,b^{12}-192\,A^2\,B\,a^2\,b^{13}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+216\,A\,B^2\,a^{11}\,b^4-108\,A\,B^2\,a^{10}\,b^5-972\,A\,B^2\,a^9\,b^6+558\,A\,B^2\,a^8\,b^7+1800\,A\,B^2\,a^7\,b^8-972\,A\,B^2\,a^6\,b^9-1548\,A\,B^2\,a^5\,b^{10}+648\,A\,B^2\,a^4\,b^{11}+504\,A\,B^2\,a^3\,b^{12}-864\,A\,B\,C\,a^{12}\,b^3+432\,A\,B\,C\,a^{11}\,b^4+3816\,A\,B\,C\,a^{10}\,b^5-2160\,A\,B\,C\,a^9\,b^6-6840\,A\,B\,C\,a^8\,b^7+3642\,A\,B\,C\,a^7\,b^8+5568\,A\,B\,C\,a^6\,b^9-2268\,A\,B\,C\,a^5\,b^{10}-1560\,A\,B\,C\,a^4\,b^{11}-24\,A\,B\,C\,a^3\,b^{12}-120\,A\,B\,C\,a^2\,b^{13}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}-216\,B^3\,a^{12}\,b^3+108\,B^3\,a^{11}\,b^4+972\,B^3\,a^{10}\,b^5-486\,B^3\,a^9\,b^6-1728\,B^3\,a^8\,b^7+756\,B^3\,a^7\,b^8+1404\,B^3\,a^6\,b^9-432\,B^3\,a^5\,b^{10}-432\,B^3\,a^4\,b^{11}+1296\,B^2\,C\,a^{13}\,b^2-648\,B^2\,C\,a^{12}\,b^3-5724\,B^2\,C\,a^{11}\,b^4+2808\,B^2\,C\,a^{10}\,b^5+9828\,B^2\,C\,a^9\,b^6-4203\,B^2\,C\,a^8\,b^7-7524\,B^2\,C\,a^7\,b^8+2268\,B^2\,C\,a^6\,b^9+1980\,B^2\,C\,a^5\,b^{10}+144\,B^2\,C\,a^3\,b^{12}-2592\,B\,C^2\,a^{14}\,b+1296\,B\,C^2\,a^{13}\,b^2+11232\,B\,C^2\,a^{12}\,b^3-5400\,B\,C^2\,a^{11}\,b^4-18594\,B\,C^2\,a^{10}\,b^5+7767\,B\,C^2\,a^9\,b^6+13347\,B\,C^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,A\,B\,C\,a^5\,b^{10}-1560\,A\,B\,C\,a^4\,b^{11}-24\,A\,B\,C\,a^3\,b^{12}-120\,A\,B\,C\,a^2\,b^{13}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}-216\,B^3\,a^{12}\,b^3+108\,B^3\,a^{11}\,b^4+972\,B^3\,a^{10}\,b^5-486\,B^3\,a^9\,b^6-1728\,B^3\,a^8\,b^7+756\,B^3\,a^7\,b^8+1404\,B^3\,a^6\,b^9-432\,B^3\,a^5\,b^{10}-432\,B^3\,a^4\,b^{11}+1296\,B^2\,C\,a^{13}\,b^2-648\,B^2\,C\,a^{12}\,b^3-5724\,B^2\,C\,a^{11}\,b^4+2808\,B^2\,C\,a^{10}\,b^5+9828\,B^2\,C\,a^9\,b^6-4203\,B^2\,C\,a^8\,b^7-7524\,B^2\,C\,a^7\,b^8+2268\,B^2\,C\,a^6\,b^9+1980\,B^2\,C\,a^5\,b^{10}+144\,B^2\,C\,a^3\,b^{12}-2592\,B\,C^2\,a^{14}\,b+1296\,B\,C^2\,a^{13}\,b^2+11232\,B\,C^2\,a^{12}\,b^3-5400\,B\,C^2\,a^{11}\,b^4-18594\,B\,C^2\,a^{10}\,b^5+7767\,B\,C^2\,a^9\,b^6+13347\,B\,C^2\,a^8\,b^7-3972\,B\,C^2\,a^7\,b^8-2892\,B\,C^2\,a^6\,b^9+9\,B\,C^2\,a^5\,b^{10}-489\,B\,C^2\,a^4\,b^{11}+12\,B\,C^2\,a^3\,b^{12}-12\,B\,C^2\,a^2\,b^{13}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{a\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*B*b^7 + 36*C*a^7 + 3*C*b^7 - 6*A*a^2*b^5 - 15*A*a^3*b^4 + 3*A*a^4*b^3 + 6*A*a^5*b^2 - 10*B*a^2*b^5 + 16*B*a^3*b^4 + 35*B*a^4*b^3 - 9*B*a^5*b^2 + 5*C*a^2*b^5 + 26*C*a^3*b^4 - 29*C*a^4*b^3 - 67*C*a^5*b^2 - 4*B*a*b^6 - 18*B*a^6*b - 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^5*(3*C*b^7 - 36*C*a^7 - 2*B*b^7 - 6*A*a^2*b^5 + 15*A*a^3*b^4 + 3*A*a^4*b^3 - 6*A*a^5*b^2 + 10*B*a^2*b^5 + 16*B*a^3*b^4 - 35*B*a^4*b^3 - 9*B*a^5*b^2 + 5*C*a^2*b^5 - 26*C*a^3*b^4 - 29*C*a^4*b^3 + 67*C*a^5*b^2 - 4*B*a*b^6 + 18*B*a^6*b + 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^7*(C*b^6 - 12*C*a^6 - 2*B*b^6 + 6*A*a^2*b^4 + A*a^3*b^3 - 2*A*a^4*b^2 + 4*B*a^2*b^4 - 12*B*a^3*b^3 - 3*B*a^4*b^2 - 8*C*a^2*b^4 - 10*C*a^3*b^3 + 23*C*a^4*b^2 + 2*B*a*b^5 + 6*B*a^5*b + 5*C*a*b^5 + 6*C*a^5*b))/((a*b^4 - b^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*b^6 - 12*C*a^6 + C*b^6 + 6*A*a^2*b^4 - A*a^3*b^3 - 2*A*a^4*b^2 - 4*B*a^2*b^4 - 12*B*a^3*b^3 + 3*B*a^4*b^2 - 8*C*a^2*b^4 + 10*C*a^3*b^3 + 23*C*a^4*b^2 + 2*B*a*b^5 + 6*B*a^5*b - 5*C*a*b^5 - 6*C*a^5*b))/((a + b)*(b^6 - 2*a*b^5 + a^2*b^4)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(6*a^2 - 2*b^2) - tan(c/2 + (d*x)/2)^2*(4*a*b + 4*a^2) + tan(c/2 + (d*x)/2)^6*(4*a*b - 4*a^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan(((((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b))/b^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*1i)/b^5 - (((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b))/b^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*1i)/b^5)/((8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 - 432*B^3*a^4*b^11 - 432*B^3*a^5*b^10 + 1404*B^3*a^6*b^9 + 756*B^3*a^7*b^8 - 1728*B^3*a^8*b^7 - 486*B^3*a^9*b^6 + 972*B^3*a^10*b^5 + 108*B^3*a^11*b^4 - 216*B^3*a^12*b^3 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 2592*B*C^2*a^14*b + 504*A*B^2*a^3*b^12 + 648*A*B^2*a^4*b^11 - 1548*A*B^2*a^5*b^10 - 972*A*B^2*a^6*b^9 + 1800*A*B^2*a^7*b^8 + 558*A*B^2*a^8*b^7 - 972*A*B^2*a^9*b^6 - 108*A*B^2*a^10*b^5 + 216*A*B^2*a^11*b^4 - 192*A^2*B*a^2*b^13 - 312*A^2*B*a^3*b^12 + 564*A^2*B*a^4*b^11 + 396*A^2*B*a^5*b^10 - 624*A^2*B*a^6*b^9 - 210*A^2*B*a^7*b^8 + 324*A^2*B*a^8*b^7 + 36*A^2*B*a^9*b^6 - 72*A^2*B*a^10*b^5 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4 - 12*B*C^2*a^2*b^13 + 12*B*C^2*a^3*b^12 - 489*B*C^2*a^4*b^11 + 9*B*C^2*a^5*b^10 - 2892*B*C^2*a^6*b^9 - 3972*B*C^2*a^7*b^8 + 13347*B*C^2*a^8*b^7 + 7767*B*C^2*a^9*b^6 - 18594*B*C^2*a^10*b^5 - 5400*B*C^2*a^11*b^4 + 11232*B*C^2*a^12*b^3 + 1296*B*C^2*a^13*b^2 + 144*B^2*C*a^3*b^12 + 1980*B^2*C*a^5*b^10 + 2268*B^2*C*a^6*b^9 - 7524*B^2*C*a^7*b^8 - 4203*B^2*C*a^8*b^7 + 9828*B^2*C*a^9*b^6 + 2808*B^2*C*a^10*b^5 - 5724*B^2*C*a^11*b^4 - 648*B^2*C*a^12*b^3 + 1296*B^2*C*a^13*b^2 - 120*A*B*C*a^2*b^13 - 24*A*B*C*a^3*b^12 - 1560*A*B*C*a^4*b^11 - 2268*A*B*C*a^5*b^10 + 5568*A*B*C*a^6*b^9 + 3642*A*B*C*a^7*b^8 - 6840*A*B*C*a^8*b^7 - 2160*A*B*C*a^9*b^6 + 3816*A*B*C*a^10*b^5 + 432*A*B*C*a^11*b^4 - 864*A*B*C*a^12*b^3))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b))/b^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b))/b^5 + (((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b))/b^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b))/b^5))*(6*C*a^2 + b^2*(A + C/2) - 3*B*a*b)*2i)/(b^5*d) - (a*atan(((a*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 - 432*B^3*a^4*b^11 - 432*B^3*a^5*b^10 + 1404*B^3*a^6*b^9 + 756*B^3*a^7*b^8 - 1728*B^3*a^8*b^7 - 486*B^3*a^9*b^6 + 972*B^3*a^10*b^5 + 108*B^3*a^11*b^4 - 216*B^3*a^12*b^3 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 2592*B*C^2*a^14*b + 504*A*B^2*a^3*b^12 + 648*A*B^2*a^4*b^11 - 1548*A*B^2*a^5*b^10 - 972*A*B^2*a^6*b^9 + 1800*A*B^2*a^7*b^8 + 558*A*B^2*a^8*b^7 - 972*A*B^2*a^9*b^6 - 108*A*B^2*a^10*b^5 + 216*A*B^2*a^11*b^4 - 192*A^2*B*a^2*b^13 - 312*A^2*B*a^3*b^12 + 564*A^2*B*a^4*b^11 + 396*A^2*B*a^5*b^10 - 624*A^2*B*a^6*b^9 - 210*A^2*B*a^7*b^8 + 324*A^2*B*a^8*b^7 + 36*A^2*B*a^9*b^6 - 72*A^2*B*a^10*b^5 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4 - 12*B*C^2*a^2*b^13 + 12*B*C^2*a^3*b^12 - 489*B*C^2*a^4*b^11 + 9*B*C^2*a^5*b^10 - 2892*B*C^2*a^6*b^9 - 3972*B*C^2*a^7*b^8 + 13347*B*C^2*a^8*b^7 + 7767*B*C^2*a^9*b^6 - 18594*B*C^2*a^10*b^5 - 5400*B*C^2*a^11*b^4 + 11232*B*C^2*a^12*b^3 + 1296*B*C^2*a^13*b^2 + 144*B^2*C*a^3*b^12 + 1980*B^2*C*a^5*b^10 + 2268*B^2*C*a^6*b^9 - 7524*B^2*C*a^7*b^8 - 4203*B^2*C*a^8*b^7 + 9828*B^2*C*a^9*b^6 + 2808*B^2*C*a^10*b^5 - 5724*B^2*C*a^11*b^4 - 648*B^2*C*a^12*b^3 + 1296*B^2*C*a^13*b^2 - 120*A*B*C*a^2*b^13 - 24*A*B*C*a^3*b^12 - 1560*A*B*C*a^4*b^11 - 2268*A*B*C*a^5*b^10 + 5568*A*B*C*a^6*b^9 + 3642*A*B*C*a^7*b^8 - 6840*A*B*C*a^8*b^7 - 2160*A*B*C*a^9*b^6 + 3816*A*B*C*a^10*b^5 + 432*A*B*C*a^11*b^4 - 864*A*B*C*a^12*b^3))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (a*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*1i)/(d*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))","B"
917,1,11393,323,17.606124,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^3),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^5+2\,C\,b^5+A\,a^2\,b^3+6\,B\,a^2\,b^3-B\,a^3\,b^2-4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-4\,A\,a\,b^4-2\,B\,a^4\,b+2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,b^5-6\,C\,a^5+A\,a^2\,b^3-6\,B\,a^2\,b^3-B\,a^3\,b^2-4\,C\,a^2\,b^3+12\,C\,a^3\,b^2+4\,A\,a\,b^4+2\,B\,a^4\,b-2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,b^6-6\,C\,a^6+3\,A\,a^2\,b^4-5\,B\,a^3\,b^3-6\,C\,a^2\,b^4+13\,C\,a^4\,b^2+2\,B\,a^5\,b\right)}{b\,\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(-A^2\,B\,a^4\,b^8-4\,A^2\,B\,a^2\,b^{10}-4\,A^2\,B\,b^{12}+3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+2\,A\,B^2\,a^7\,b^5+2\,A\,B^2\,a^6\,b^6-2\,A\,B^2\,a^5\,b^7-2\,A\,B^2\,a^3\,b^9-6\,A\,B^2\,a^2\,b^{10}+20\,A\,B^2\,a\,b^{11}+4\,A\,B^2\,b^{12}-12\,A\,B\,C\,a^8\,b^4-12\,A\,B\,C\,a^7\,b^5+12\,A\,B\,C\,a^6\,b^6+24\,A\,B\,C\,a^4\,b^8+36\,A\,B\,C\,a^3\,b^9-96\,A\,B\,C\,a^2\,b^{10}-24\,A\,B\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}-4\,B^3\,a^9\,b^3+2\,B^3\,a^8\,b^4+18\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6-36\,B^3\,a^5\,b^7+26\,B^3\,a^4\,b^8+34\,B^3\,a^3\,b^9-24\,B^3\,a^2\,b^{10}-12\,B^3\,a\,b^{11}+36\,B^2\,C\,a^{10}\,b^2-18\,B^2\,C\,a^9\,b^3-162\,B^2\,C\,a^8\,b^4+105\,B^2\,C\,a^7\,b^5+312\,B^2\,C\,a^6\,b^6-198\,B^2\,C\,a^5\,b^7-282\,B^2\,C\,a^4\,b^8+156\,B^2\,C\,a^3\,b^9+96\,B^2\,C\,a^2\,b^{10}-108\,B\,C^2\,a^{11}\,b+54\,B\,C^2\,a^{10}\,b^2+486\,B\,C^2\,a^9\,b^3-279\,B\,C^2\,a^8\,b^4-900\,B\,C^2\,a^7\,b^5+486\,B\,C^2\,a^6\,b^6+774\,B\,C^2\,a^5\,b^7-324\,B\,C^2\,a^4\,b^8-252\,B\,C^2\,a^3\,b^9+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)}{b^4}+\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(B\,b-3\,C\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-3\,C\,a\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)}{b^4}\right)}{b^4}}\right)\,\left(B\,b-3\,C\,a\right)\,2{}\mathrm{i}}{b^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(-A^2\,B\,a^4\,b^8-4\,A^2\,B\,a^2\,b^{10}-4\,A^2\,B\,b^{12}+3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+2\,A\,B^2\,a^7\,b^5+2\,A\,B^2\,a^6\,b^6-2\,A\,B^2\,a^5\,b^7-2\,A\,B^2\,a^3\,b^9-6\,A\,B^2\,a^2\,b^{10}+20\,A\,B^2\,a\,b^{11}+4\,A\,B^2\,b^{12}-12\,A\,B\,C\,a^8\,b^4-12\,A\,B\,C\,a^7\,b^5+12\,A\,B\,C\,a^6\,b^6+24\,A\,B\,C\,a^4\,b^8+36\,A\,B\,C\,a^3\,b^9-96\,A\,B\,C\,a^2\,b^{10}-24\,A\,B\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}-4\,B^3\,a^9\,b^3+2\,B^3\,a^8\,b^4+18\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6-36\,B^3\,a^5\,b^7+26\,B^3\,a^4\,b^8+34\,B^3\,a^3\,b^9-24\,B^3\,a^2\,b^{10}-12\,B^3\,a\,b^{11}+36\,B^2\,C\,a^{10}\,b^2-18\,B^2\,C\,a^9\,b^3-162\,B^2\,C\,a^8\,b^4+105\,B^2\,C\,a^7\,b^5+312\,B^2\,C\,a^6\,b^6-198\,B^2\,C\,a^5\,b^7-282\,B^2\,C\,a^4\,b^8+156\,B^2\,C\,a^3\,b^9+96\,B^2\,C\,a^2\,b^{10}-108\,B\,C^2\,a^{11}\,b+54\,B\,C^2\,a^{10}\,b^2+486\,B\,C^2\,a^9\,b^3-279\,B\,C^2\,a^8\,b^4-900\,B\,C^2\,a^7\,b^5+486\,B\,C^2\,a^6\,b^6+774\,B\,C^2\,a^5\,b^7-324\,B\,C^2\,a^4\,b^8-252\,B\,C^2\,a^3\,b^9+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(6*C*a^5 + 2*C*b^5 + A*a^2*b^3 + 6*B*a^2*b^3 - B*a^3*b^2 - 4*C*a^2*b^3 - 12*C*a^3*b^2 - 4*A*a*b^4 - 2*B*a^4*b + 2*C*a*b^4 + 3*C*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) - (tan(c/2 + (d*x)/2)^5*(2*C*b^5 - 6*C*a^5 + A*a^2*b^3 - 6*B*a^2*b^3 - B*a^3*b^2 - 4*C*a^2*b^3 + 12*C*a^3*b^2 + 4*A*a*b^4 + 2*B*a^4*b - 2*C*a*b^4 + 3*C*a^4*b))/((a*b^3 - b^4)*(a + b)^2) + (2*tan(c/2 + (d*x)/2)^3*(2*C*b^6 - 6*C*a^6 + 3*A*a^2*b^4 - 5*B*a^3*b^3 - 6*C*a^2*b^4 + 13*C*a^4*b^2 + 2*B*a^5*b))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) + (atan((((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + ((B*b - 3*C*a)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4)*1i)/b^4 + ((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - ((B*b - 3*C*a)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4)*1i)/b^4)/((16*(108*C^3*a^12 + 4*A*B^2*b^12 - 4*A^2*B*b^12 - 12*B^3*a*b^11 - 54*C^3*a^11*b - 24*B^3*a^2*b^10 + 34*B^3*a^3*b^9 + 26*B^3*a^4*b^8 - 36*B^3*a^5*b^7 - 13*B^3*a^6*b^6 + 18*B^3*a^7*b^5 + 2*B^3*a^8*b^4 - 4*B^3*a^9*b^3 + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 20*A*B^2*a*b^11 + 12*A^2*C*a*b^11 - 108*B*C^2*a^11*b - 6*A*B^2*a^2*b^10 - 2*A*B^2*a^3*b^9 - 2*A*B^2*a^5*b^7 + 2*A*B^2*a^6*b^6 + 2*A*B^2*a^7*b^5 - 4*A^2*B*a^2*b^10 - A^2*B*a^4*b^8 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7 - 252*B*C^2*a^3*b^9 - 324*B*C^2*a^4*b^8 + 774*B*C^2*a^5*b^7 + 486*B*C^2*a^6*b^6 - 900*B*C^2*a^7*b^5 - 279*B*C^2*a^8*b^4 + 486*B*C^2*a^9*b^3 + 54*B*C^2*a^10*b^2 + 96*B^2*C*a^2*b^10 + 156*B^2*C*a^3*b^9 - 282*B^2*C*a^4*b^8 - 198*B^2*C*a^5*b^7 + 312*B^2*C*a^6*b^6 + 105*B^2*C*a^7*b^5 - 162*B^2*C*a^8*b^4 - 18*B^2*C*a^9*b^3 + 36*B^2*C*a^10*b^2 - 24*A*B*C*a*b^11 - 96*A*B*C*a^2*b^10 + 36*A*B*C*a^3*b^9 + 24*A*B*C*a^4*b^8 + 12*A*B*C*a^6*b^6 - 12*A*B*C*a^7*b^5 - 12*A*B*C*a^8*b^4))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - ((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + ((B*b - 3*C*a)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4))/b^4 + ((B*b - 3*C*a)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - ((B*b - 3*C*a)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (8*tan(c/2 + (d*x)/2)*(B*b - 3*C*a)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6))))/b^4))/b^4))*(B*b - 3*C*a)*2i)/(b^4*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(108*C^3*a^12 + 4*A*B^2*b^12 - 4*A^2*B*b^12 - 12*B^3*a*b^11 - 54*C^3*a^11*b - 24*B^3*a^2*b^10 + 34*B^3*a^3*b^9 + 26*B^3*a^4*b^8 - 36*B^3*a^5*b^7 - 13*B^3*a^6*b^6 + 18*B^3*a^7*b^5 + 2*B^3*a^8*b^4 - 4*B^3*a^9*b^3 + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 20*A*B^2*a*b^11 + 12*A^2*C*a*b^11 - 108*B*C^2*a^11*b - 6*A*B^2*a^2*b^10 - 2*A*B^2*a^3*b^9 - 2*A*B^2*a^5*b^7 + 2*A*B^2*a^6*b^6 + 2*A*B^2*a^7*b^5 - 4*A^2*B*a^2*b^10 - A^2*B*a^4*b^8 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7 - 252*B*C^2*a^3*b^9 - 324*B*C^2*a^4*b^8 + 774*B*C^2*a^5*b^7 + 486*B*C^2*a^6*b^6 - 900*B*C^2*a^7*b^5 - 279*B*C^2*a^8*b^4 + 486*B*C^2*a^9*b^3 + 54*B*C^2*a^10*b^2 + 96*B^2*C*a^2*b^10 + 156*B^2*C*a^3*b^9 - 282*B^2*C*a^4*b^8 - 198*B^2*C*a^5*b^7 + 312*B^2*C*a^6*b^6 + 105*B^2*C*a^7*b^5 - 162*B^2*C*a^8*b^4 - 18*B^2*C*a^9*b^3 + 36*B^2*C*a^10*b^2 - 24*A*B*C*a*b^11 - 96*A*B*C*a^2*b^10 + 36*A*B*C*a^3*b^9 + 24*A*B*C*a^4*b^8 + 12*A*B*C*a^6*b^6 - 12*A*B*C*a^7*b^5 - 12*A*B*C*a^8*b^4))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*1i)/(d*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
918,1,8128,242,15.911995,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2-B\,a^2\,b^2+6\,C\,a^2\,b^2+A\,a\,b^3-4\,B\,a\,b^3+C\,a^3\,b\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2+B\,a^2\,b^2+6\,C\,a^2\,b^2-A\,a\,b^3-4\,B\,a\,b^3-C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7-6\,A\,B\,C\,a^3\,b^6-12\,A\,B\,C\,a\,b^8+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}\right)}{b^3}-\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)}{b^3}\right)}{b^3}}\right)\,2{}\mathrm{i}}{b^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7-6\,A\,B\,C\,a^3\,b^6-12\,A\,B\,C\,a\,b^8+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^3*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 - B*a^2*b^2 + 6*C*a^2*b^2 + A*a*b^3 - 4*B*a*b^3 + C*a^3*b))/((a*b^2 - b^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 + B*a^2*b^2 + 6*C*a^2*b^2 - A*a*b^3 - 4*B*a*b^3 - C*a^3*b))/((a + b)*(b^4 - 2*a*b^3 + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (C*atan(((C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3)*1i)/b^3 + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3)*1i)/b^3)/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 - 20*B*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5 - 12*A*B*C*a*b^8 - 6*A*B*C*a^3*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3))/b^3 - (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))))/b^3))/b^3))*2i)/(b^3*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 - 20*B*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5 - 12*A*B*C*a*b^8 - 6*A*B*C*a^3*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*1i)/(d*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
919,1,280,202,7.836860,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^2-2\,B\,a^2-2\,B\,b^2+C\,a^2+4\,A\,a\,b-B\,a\,b+4\,C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^2+2\,B\,a^2+2\,B\,b^2+C\,a^2-4\,A\,a\,b-B\,a\,b-4\,C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,A\,a^2+A\,b^2+C\,a^2+2\,C\,b^2-3\,B\,a\,b\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(A*b^2 - 2*B*a^2 - 2*B*b^2 + C*a^2 + 4*A*a*b - B*a*b + 4*C*a*b))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 + C*a^2 - 4*A*a*b - B*a*b - 4*C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atanh((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*A*a^2 + A*b^2 + C*a^2 + 2*C*b^2 - 3*B*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
920,1,8147,229,17.180612,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^4-2\,A\,b^4+6\,A\,a^2\,b^2-B\,a^2\,b^2+2\,C\,a^2\,b^2+A\,a\,b^3-4\,B\,a^3\,b+C\,a^3\,b\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4-6\,A\,a^2\,b^2-B\,a^2\,b^2-2\,C\,a^2\,b^2+A\,a\,b^3+4\,B\,a^3\,b+C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{2\,A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)}{a^3}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)}{a^3}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9-4\,A^2\,B\,a^9-20\,A^2\,B\,a^8\,b+6\,A^2\,B\,a^7\,b^2+2\,A^2\,B\,a^6\,b^3+2\,A^2\,B\,a^4\,b^5-2\,A^2\,B\,a^3\,b^6-2\,A^2\,B\,a^2\,b^7+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^2\,a^5\,b^4-12\,A\,B\,C\,a^8\,b-6\,A\,B\,C\,a^6\,b^3+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}\right)}{a^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9-4\,A^2\,B\,a^9-20\,A^2\,B\,a^8\,b+6\,A^2\,B\,a^7\,b^2+2\,A^2\,B\,a^6\,b^3+2\,A^2\,B\,a^4\,b^5-2\,A^2\,B\,a^3\,b^6-2\,A^2\,B\,a^2\,b^7+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^2\,a^5\,b^4-12\,A\,B\,C\,a^8\,b-6\,A\,B\,C\,a^6\,b^3+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*C*a^4 - 2*A*b^4 + 6*A*a^2*b^2 - B*a^2*b^2 + 2*C*a^2*b^2 + A*a*b^3 - 4*B*a^3*b + C*a^3*b))/((a^2*b - a^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 - 6*A*a^2*b^2 - B*a^2*b^2 - 2*C*a^2*b^2 + A*a*b^3 + 4*B*a^3*b + C*a^3*b))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (2*A*atan(((A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3))/a^3 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3))/a^3)/((16*(4*A^3*b^9 + 4*A*B^2*a^9 - 4*A^2*B*a^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 - 20*A^2*B*a^8*b + 6*A^2*C*a^8*b + A*B^2*a^5*b^4 + 4*A*B^2*a^7*b^2 - 2*A^2*B*a^2*b^7 - 2*A^2*B*a^3*b^6 + 2*A^2*B*a^4*b^5 + 2*A^2*B*a^6*b^3 + 6*A^2*B*a^7*b^2 + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2 - 12*A*B*C*a^8*b - 6*A*B*C*a^6*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3)*1i)/a^3 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2)*8i)/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*1i)/a^3)*1i)/a^3)))/(a^3*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(4*A^3*b^9 + 4*A*B^2*a^9 - 4*A^2*B*a^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 - 20*A^2*B*a^8*b + 6*A^2*C*a^8*b + A*B^2*a^5*b^4 + 4*A*B^2*a^7*b^2 - 2*A^2*B*a^2*b^7 - 2*A^2*B*a^3*b^6 + 2*A^2*B*a^4*b^5 + 2*A^2*B*a^6*b^3 + 6*A^2*B*a^7*b^2 + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2 - 12*A*B*C*a^8*b - 6*A*B*C*a^6*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
921,1,6708,330,11.074671,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^5+6\,A\,b^5-12\,A\,a^2\,b^3-4\,A\,a^3\,b^2-B\,a^2\,b^3+6\,B\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4+2\,A\,a^4\,b-2\,B\,a\,b^4-4\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^5-6\,A\,b^5+12\,A\,a^2\,b^3-4\,A\,a^3\,b^2-B\,a^2\,b^3-6\,B\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4-2\,A\,a^4\,b+2\,B\,a\,b^4+4\,C\,a^4\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^6-6\,A\,b^6+13\,A\,a^2\,b^4-6\,A\,a^4\,b^2-5\,B\,a^3\,b^3+3\,C\,a^4\,b^2+2\,B\,a\,b^5\right)}{a\,\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(3\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(A\,b\,3{}\mathrm{i}-B\,a\,1{}\mathrm{i}\right)}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}-252\,A^2\,B\,a^9\,b^3-324\,A^2\,B\,a^8\,b^4+774\,A^2\,B\,a^7\,b^5+486\,A^2\,B\,a^6\,b^6-900\,A^2\,B\,a^5\,b^7-279\,A^2\,B\,a^4\,b^8+486\,A^2\,B\,a^3\,b^9+54\,A^2\,B\,a^2\,b^{10}-108\,A^2\,B\,a\,b^{11}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+96\,A\,B^2\,a^{10}\,b^2+156\,A\,B^2\,a^9\,b^3-282\,A\,B^2\,a^8\,b^4-198\,A\,B^2\,a^7\,b^5+312\,A\,B^2\,a^6\,b^6+105\,A\,B^2\,a^5\,b^7-162\,A\,B^2\,a^4\,b^8-18\,A\,B^2\,a^3\,b^9+36\,A\,B^2\,a^2\,b^{10}-24\,A\,B\,C\,a^{11}\,b-96\,A\,B\,C\,a^{10}\,b^2+36\,A\,B\,C\,a^9\,b^3+24\,A\,B\,C\,a^8\,b^4+12\,A\,B\,C\,a^6\,b^6-12\,A\,B\,C\,a^5\,b^7-12\,A\,B\,C\,a^4\,b^8+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5-12\,B^3\,a^{11}\,b-24\,B^3\,a^{10}\,b^2+34\,B^3\,a^9\,b^3+26\,B^3\,a^8\,b^4-36\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6+18\,B^3\,a^5\,b^7+2\,B^3\,a^4\,b^8-4\,B^3\,a^3\,b^9+4\,B^2\,C\,a^{12}+20\,B^2\,C\,a^{11}\,b-6\,B^2\,C\,a^{10}\,b^2-2\,B^2\,C\,a^9\,b^3-2\,B^2\,C\,a^7\,b^5+2\,B^2\,C\,a^6\,b^6+2\,B^2\,C\,a^5\,b^7-4\,B\,C^2\,a^{12}-4\,B\,C^2\,a^{10}\,b^2-B\,C^2\,a^8\,b^4\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^5 + 6*A*b^5 - 12*A*a^2*b^3 - 4*A*a^3*b^2 - B*a^2*b^3 + 6*B*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 + 2*A*a^4*b - 2*B*a*b^4 - 4*C*a^4*b))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) - (tan(c/2 + (d*x)/2)^5*(2*A*a^5 - 6*A*b^5 + 12*A*a^2*b^3 - 4*A*a^3*b^2 - B*a^2*b^3 - 6*B*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 - 2*A*a^4*b + 2*B*a*b^4 + 4*C*a^4*b))/((a^3*b - a^4)*(a + b)^2) + (2*tan(c/2 + (d*x)/2)^3*(2*A*a^6 - 6*A*b^6 + 13*A*a^2*b^4 - 6*A*a^4*b^2 - 5*B*a^3*b^3 + 3*C*a^4*b^2 + 2*B*a*b^5))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) + (log(tan(c/2 + (d*x)/2) - 1i)*(3*A*b - B*a)*1i)/(a^4*d) - (log(tan(c/2 + (d*x)/2) + 1i)*(A*b*3i - B*a*1i))/(a^4*d) - (atan(((((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((16*(108*A^3*b^12 - 4*B*C^2*a^12 + 4*B^2*C*a^12 - 54*A^3*a*b^11 - 12*B^3*a^11*b - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 - 4*B^3*a^3*b^9 + 2*B^3*a^4*b^8 + 18*B^3*a^5*b^7 - 13*B^3*a^6*b^6 - 36*B^3*a^7*b^5 + 26*B^3*a^8*b^4 + 34*B^3*a^9*b^3 - 24*B^3*a^10*b^2 - 108*A^2*B*a*b^11 + 12*A*C^2*a^11*b + 20*B^2*C*a^11*b + 36*A*B^2*a^2*b^10 - 18*A*B^2*a^3*b^9 - 162*A*B^2*a^4*b^8 + 105*A*B^2*a^5*b^7 + 312*A*B^2*a^6*b^6 - 198*A*B^2*a^7*b^5 - 282*A*B^2*a^8*b^4 + 156*A*B^2*a^9*b^3 + 96*A*B^2*a^10*b^2 + 54*A^2*B*a^2*b^10 + 486*A^2*B*a^3*b^9 - 279*A^2*B*a^4*b^8 - 900*A^2*B*a^5*b^7 + 486*A^2*B*a^6*b^6 + 774*A^2*B*a^7*b^5 - 324*A^2*B*a^8*b^4 - 252*A^2*B*a^9*b^3 + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2 - B*C^2*a^8*b^4 - 4*B*C^2*a^10*b^2 + 2*B^2*C*a^5*b^7 + 2*B^2*C*a^6*b^6 - 2*B^2*C*a^7*b^5 - 2*B^2*C*a^9*b^3 - 6*B^2*C*a^10*b^2 - 24*A*B*C*a^11*b - 12*A*B*C*a^4*b^8 - 12*A*B*C*a^5*b^7 + 12*A*B*C*a^6*b^6 + 24*A*B*C*a^8*b^4 + 36*A*B*C*a^9*b^3 - 96*A*B*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*1i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
922,1,16016,453,21.932000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A\,a^7-36\,A\,b^7-2\,B\,a^7+67\,A\,a^2\,b^5-29\,A\,a^3\,b^4-26\,A\,a^4\,b^3+5\,A\,a^5\,b^2-9\,B\,a^2\,b^5-35\,B\,a^3\,b^4+16\,B\,a^4\,b^3+10\,B\,a^5\,b^2-6\,C\,a^2\,b^5+3\,C\,a^3\,b^4+15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6+4\,A\,a^6\,b+18\,B\,a\,b^6-4\,B\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^7+36\,A\,b^7+2\,B\,a^7-67\,A\,a^2\,b^5-29\,A\,a^3\,b^4+26\,A\,a^4\,b^3+5\,A\,a^5\,b^2-9\,B\,a^2\,b^5+35\,B\,a^3\,b^4+16\,B\,a^4\,b^3-10\,B\,a^5\,b^2+6\,C\,a^2\,b^5+3\,C\,a^3\,b^4-15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6-4\,A\,a^6\,b-18\,B\,a\,b^6-4\,B\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,a^6-12\,A\,b^6-2\,B\,a^6+23\,A\,a^2\,b^4-10\,A\,a^3\,b^3-8\,A\,a^4\,b^2-3\,B\,a^2\,b^4-12\,B\,a^3\,b^3+4\,B\,a^4\,b^2-2\,C\,a^2\,b^4+C\,a^3\,b^3+6\,C\,a^4\,b^2+6\,A\,a\,b^5+5\,A\,a^5\,b+6\,B\,a\,b^5+2\,B\,a^5\,b\right)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^6-12\,A\,b^6+2\,B\,a^6+23\,A\,a^2\,b^4+10\,A\,a^3\,b^3-8\,A\,a^4\,b^2+3\,B\,a^2\,b^4-12\,B\,a^3\,b^3-4\,B\,a^4\,b^2-2\,C\,a^2\,b^4-C\,a^3\,b^3+6\,C\,a^4\,b^2-6\,A\,a\,b^5-5\,A\,a^5\,b+6\,B\,a\,b^5+2\,B\,a^5\,b\right)}{\left(a+b\right)\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-6\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,b^2+4\,a\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^5}}{-\frac{8\,\left(20\,A^3\,a^{12}\,b^3-20\,A^3\,a^{11}\,b^4+411\,A^3\,a^{10}\,b^5-11\,A^3\,a^9\,b^6+1314\,A^3\,a^8\,b^7+2326\,A^3\,a^7\,b^8-7829\,A^3\,a^6\,b^9-4770\,A^3\,a^5\,b^{10}+11700\,A^3\,a^4\,b^{11}+3456\,A^3\,a^3\,b^{12}-7344\,A^3\,a^2\,b^{13}-864\,A^3\,a\,b^{14}+1728\,A^3\,b^{15}-12\,A^2\,B\,a^{13}\,b^2+12\,A^2\,B\,a^{12}\,b^3-489\,A^2\,B\,a^{11}\,b^4+9\,A^2\,B\,a^{10}\,b^5-2892\,A^2\,B\,a^9\,b^6-3972\,A^2\,B\,a^8\,b^7+13347\,A^2\,B\,a^7\,b^8+7767\,A^2\,B\,a^6\,b^9-18594\,A^2\,B\,a^5\,b^{10}-5400\,A^2\,B\,a^4\,b^{11}+11232\,A^2\,B\,a^3\,b^{12}+1296\,A^2\,B\,a^2\,b^{13}-2592\,A^2\,B\,a\,b^{14}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+144\,A\,B^2\,a^{12}\,b^3+1980\,A\,B^2\,a^{10}\,b^5+2268\,A\,B^2\,a^9\,b^6-7524\,A\,B^2\,a^8\,b^7-4203\,A\,B^2\,a^7\,b^8+9828\,A\,B^2\,a^6\,b^9+2808\,A\,B^2\,a^5\,b^{10}-5724\,A\,B^2\,a^4\,b^{11}-648\,A\,B^2\,a^3\,b^{12}+1296\,A\,B^2\,a^2\,b^{13}-120\,A\,B\,C\,a^{13}\,b^2-24\,A\,B\,C\,a^{12}\,b^3-1560\,A\,B\,C\,a^{11}\,b^4-2268\,A\,B\,C\,a^{10}\,b^5+5568\,A\,B\,C\,a^9\,b^6+3642\,A\,B\,C\,a^8\,b^7-6840\,A\,B\,C\,a^7\,b^8-2160\,A\,B\,C\,a^6\,b^9+3816\,A\,B\,C\,a^5\,b^{10}+432\,A\,B\,C\,a^4\,b^{11}-864\,A\,B\,C\,a^3\,b^{12}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}-432\,B^3\,a^{11}\,b^4-432\,B^3\,a^{10}\,b^5+1404\,B^3\,a^9\,b^6+756\,B^3\,a^8\,b^7-1728\,B^3\,a^7\,b^8-486\,B^3\,a^6\,b^9+972\,B^3\,a^5\,b^{10}+108\,B^3\,a^4\,b^{11}-216\,B^3\,a^3\,b^{12}+504\,B^2\,C\,a^{12}\,b^3+648\,B^2\,C\,a^{11}\,b^4-1548\,B^2\,C\,a^{10}\,b^5-972\,B^2\,C\,a^9\,b^6+1800\,B^2\,C\,a^8\,b^7+558\,B^2\,C\,a^7\,b^8-972\,B^2\,C\,a^6\,b^9-108\,B^2\,C\,a^5\,b^{10}+216\,B^2\,C\,a^4\,b^{11}-192\,B\,C^2\,a^{13}\,b^2-312\,B\,C^2\,a^{12}\,b^3+564\,B\,C^2\,a^{11}\,b^4+396\,B\,C^2\,a^{10}\,b^5-624\,B\,C^2\,a^9\,b^6-210\,B\,C^2\,a^8\,b^7+324\,B\,C^2\,a^7\,b^8+36\,B\,C^2\,a^6\,b^9-72\,B\,C^2\,a^5\,b^{10}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{a^5}+\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{a^5}}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-3{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,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-2892\,A^2\,B\,a^9\,b^6-3972\,A^2\,B\,a^8\,b^7+13347\,A^2\,B\,a^7\,b^8+7767\,A^2\,B\,a^6\,b^9-18594\,A^2\,B\,a^5\,b^{10}-5400\,A^2\,B\,a^4\,b^{11}+11232\,A^2\,B\,a^3\,b^{12}+1296\,A^2\,B\,a^2\,b^{13}-2592\,A^2\,B\,a\,b^{14}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+144\,A\,B^2\,a^{12}\,b^3+1980\,A\,B^2\,a^{10}\,b^5+2268\,A\,B^2\,a^9\,b^6-7524\,A\,B^2\,a^8\,b^7-4203\,A\,B^2\,a^7\,b^8+9828\,A\,B^2\,a^6\,b^9+2808\,A\,B^2\,a^5\,b^{10}-5724\,A\,B^2\,a^4\,b^{11}-648\,A\,B^2\,a^3\,b^{12}+1296\,A\,B^2\,a^2\,b^{13}-120\,A\,B\,C\,a^{13}\,b^2-24\,A\,B\,C\,a^{12}\,b^3-1560\,A\,B\,C\,a^{11}\,b^4-2268\,A\,B\,C\,a^{10}\,b^5+5568\,A\,B\,C\,a^9\,b^6+3642\,A\,B\,C\,a^8\,b^7-6840\,A\,B\,C\,a^7\,b^8-2160\,A\,B\,C\,a^6\,b^9+3816\,A\,B\,C\,a^5\,b^{10}+432\,A\,B\,C\,a^4\,b^{11}-864\,A\,B\,C\,a^3\,b^{12}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}-432\,B^3\,a^{11}\,b^4-432\,B^3\,a^{10}\,b^5+1404\,B^3\,a^9\,b^6+756\,B^3\,a^8\,b^7-1728\,B^3\,a^7\,b^8-486\,B^3\,a^6\,b^9+972\,B^3\,a^5\,b^{10}+108\,B^3\,a^4\,b^{11}-216\,B^3\,a^3\,b^{12}+504\,B^2\,C\,a^{12}\,b^3+648\,B^2\,C\,a^{11}\,b^4-1548\,B^2\,C\,a^{10}\,b^5-972\,B^2\,C\,a^9\,b^6+1800\,B^2\,C\,a^8\,b^7+558\,B^2\,C\,a^7\,b^8-972\,B^2\,C\,a^6\,b^9-108\,B^2\,C\,a^5\,b^{10}+216\,B^2\,C\,a^4\,b^{11}-192\,B\,C^2\,a^{13}\,b^2-312\,B\,C^2\,a^{12}\,b^3+564\,B\,C^2\,a^{11}\,b^4+396\,B\,C^2\,a^{10}\,b^5-624\,B\,C^2\,a^9\,b^6-210\,B\,C^2\,a^8\,b^7+324\,B\,C^2\,a^7\,b^8+36\,B\,C^2\,a^6\,b^9-72\,B\,C^2\,a^5\,b^{10}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(3*A*a^7 - 36*A*b^7 - 2*B*a^7 + 67*A*a^2*b^5 - 29*A*a^3*b^4 - 26*A*a^4*b^3 + 5*A*a^5*b^2 - 9*B*a^2*b^5 - 35*B*a^3*b^4 + 16*B*a^4*b^3 + 10*B*a^5*b^2 - 6*C*a^2*b^5 + 3*C*a^3*b^4 + 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 + 4*A*a^6*b + 18*B*a*b^6 - 4*B*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^3*(3*A*a^7 + 36*A*b^7 + 2*B*a^7 - 67*A*a^2*b^5 - 29*A*a^3*b^4 + 26*A*a^4*b^3 + 5*A*a^5*b^2 - 9*B*a^2*b^5 + 35*B*a^3*b^4 + 16*B*a^4*b^3 - 10*B*a^5*b^2 + 6*C*a^2*b^5 + 3*C*a^3*b^4 - 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 - 4*A*a^6*b - 18*B*a*b^6 - 4*B*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) + (tan(c/2 + (d*x)/2)^7*(A*a^6 - 12*A*b^6 - 2*B*a^6 + 23*A*a^2*b^4 - 10*A*a^3*b^3 - 8*A*a^4*b^2 - 3*B*a^2*b^4 - 12*B*a^3*b^3 + 4*B*a^4*b^2 - 2*C*a^2*b^4 + C*a^3*b^3 + 6*C*a^4*b^2 + 6*A*a*b^5 + 5*A*a^5*b + 6*B*a*b^5 + 2*B*a^5*b))/((a^4*b - a^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(A*a^6 - 12*A*b^6 + 2*B*a^6 + 23*A*a^2*b^4 + 10*A*a^3*b^3 - 8*A*a^4*b^2 + 3*B*a^2*b^4 - 12*B*a^3*b^3 - 4*B*a^4*b^2 - 2*C*a^2*b^4 - C*a^3*b^3 + 6*C*a^4*b^2 - 6*A*a*b^5 - 5*A*a^5*b + 6*B*a*b^5 + 2*B*a^5*b))/((a + b)*(a^6 - 2*a^5*b + a^4*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^4*(2*a^2 - 6*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*b^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (atan(((((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i))/a^5 + (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*1i)/a^5 - (((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i))/a^5 - (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*1i)/a^5)/((((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i))/a^5 + (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i))/a^5 - (8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 - 216*B^3*a^3*b^12 + 108*B^3*a^4*b^11 + 972*B^3*a^5*b^10 - 486*B^3*a^6*b^9 - 1728*B^3*a^7*b^8 + 756*B^3*a^8*b^7 + 1404*B^3*a^9*b^6 - 432*B^3*a^10*b^5 - 432*B^3*a^11*b^4 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 - 2592*A^2*B*a*b^14 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 1296*A*B^2*a^2*b^13 - 648*A*B^2*a^3*b^12 - 5724*A*B^2*a^4*b^11 + 2808*A*B^2*a^5*b^10 + 9828*A*B^2*a^6*b^9 - 4203*A*B^2*a^7*b^8 - 7524*A*B^2*a^8*b^7 + 2268*A*B^2*a^9*b^6 + 1980*A*B^2*a^10*b^5 + 144*A*B^2*a^12*b^3 + 1296*A^2*B*a^2*b^13 + 11232*A^2*B*a^3*b^12 - 5400*A^2*B*a^4*b^11 - 18594*A^2*B*a^5*b^10 + 7767*A^2*B*a^6*b^9 + 13347*A^2*B*a^7*b^8 - 3972*A^2*B*a^8*b^7 - 2892*A^2*B*a^9*b^6 + 9*A^2*B*a^10*b^5 - 489*A^2*B*a^11*b^4 + 12*A^2*B*a^12*b^3 - 12*A^2*B*a^13*b^2 + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2 - 72*B*C^2*a^5*b^10 + 36*B*C^2*a^6*b^9 + 324*B*C^2*a^7*b^8 - 210*B*C^2*a^8*b^7 - 624*B*C^2*a^9*b^6 + 396*B*C^2*a^10*b^5 + 564*B*C^2*a^11*b^4 - 312*B*C^2*a^12*b^3 - 192*B*C^2*a^13*b^2 + 216*B^2*C*a^4*b^11 - 108*B^2*C*a^5*b^10 - 972*B^2*C*a^6*b^9 + 558*B^2*C*a^7*b^8 + 1800*B^2*C*a^8*b^7 - 972*B^2*C*a^9*b^6 - 1548*B^2*C*a^10*b^5 + 648*B^2*C*a^11*b^4 + 504*B^2*C*a^12*b^3 - 864*A*B*C*a^3*b^12 + 432*A*B*C*a^4*b^11 + 3816*A*B*C*a^5*b^10 - 2160*A*B*C*a^6*b^9 - 6840*A*B*C*a^7*b^8 + 3642*A*B*C*a^8*b^7 + 5568*A*B*C*a^9*b^6 - 2268*A*B*C*a^10*b^5 - 1560*A*B*C*a^11*b^4 - 24*A*B*C*a^12*b^3 - 120*A*B*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i))/a^5 - (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i))/a^5))*(A*b^2*6i + a^2*((A*1i)/2 + C*1i) - B*a*b*3i)*2i)/(a^5*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 - 216*B^3*a^3*b^12 + 108*B^3*a^4*b^11 + 972*B^3*a^5*b^10 - 486*B^3*a^6*b^9 - 1728*B^3*a^7*b^8 + 756*B^3*a^8*b^7 + 1404*B^3*a^9*b^6 - 432*B^3*a^10*b^5 - 432*B^3*a^11*b^4 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 - 2592*A^2*B*a*b^14 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 1296*A*B^2*a^2*b^13 - 648*A*B^2*a^3*b^12 - 5724*A*B^2*a^4*b^11 + 2808*A*B^2*a^5*b^10 + 9828*A*B^2*a^6*b^9 - 4203*A*B^2*a^7*b^8 - 7524*A*B^2*a^8*b^7 + 2268*A*B^2*a^9*b^6 + 1980*A*B^2*a^10*b^5 + 144*A*B^2*a^12*b^3 + 1296*A^2*B*a^2*b^13 + 11232*A^2*B*a^3*b^12 - 5400*A^2*B*a^4*b^11 - 18594*A^2*B*a^5*b^10 + 7767*A^2*B*a^6*b^9 + 13347*A^2*B*a^7*b^8 - 3972*A^2*B*a^8*b^7 - 2892*A^2*B*a^9*b^6 + 9*A^2*B*a^10*b^5 - 489*A^2*B*a^11*b^4 + 12*A^2*B*a^12*b^3 - 12*A^2*B*a^13*b^2 + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2 - 72*B*C^2*a^5*b^10 + 36*B*C^2*a^6*b^9 + 324*B*C^2*a^7*b^8 - 210*B*C^2*a^8*b^7 - 624*B*C^2*a^9*b^6 + 396*B*C^2*a^10*b^5 + 564*B*C^2*a^11*b^4 - 312*B*C^2*a^12*b^3 - 192*B*C^2*a^13*b^2 + 216*B^2*C*a^4*b^11 - 108*B^2*C*a^5*b^10 - 972*B^2*C*a^6*b^9 + 558*B^2*C*a^7*b^8 + 1800*B^2*C*a^8*b^7 - 972*B^2*C*a^9*b^6 - 1548*B^2*C*a^10*b^5 + 648*B^2*C*a^11*b^4 + 504*B^2*C*a^12*b^3 - 864*A*B*C*a^3*b^12 + 432*A*B*C*a^4*b^11 + 3816*A*B*C*a^5*b^10 - 2160*A*B*C*a^6*b^9 - 6840*A*B*C*a^7*b^8 + 3642*A*B*C*a^8*b^7 + 5568*A*B*C*a^9*b^6 - 2268*A*B*C*a^10*b^5 - 1560*A*B*C*a^11*b^4 - 24*A*B*C*a^12*b^3 - 120*A*B*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*1i)/(d*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))","B"
923,1,15959,470,20.923496,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b/cos(c + d*x))^4),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,C\,a^7+2\,C\,b^7+3\,A\,a^2\,b^5+2\,A\,a^3\,b^4-12\,B\,a^2\,b^5-4\,B\,a^3\,b^4+6\,B\,a^4\,b^3+B\,a^5\,b^2-6\,C\,a^2\,b^5+26\,C\,a^3\,b^4+11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,B\,a^6\,b-2\,C\,a\,b^6-4\,C\,a^6\,b\right)}{b^4\,{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,C\,a^7-2\,C\,b^7-3\,A\,a^2\,b^5+2\,A\,a^3\,b^4-12\,B\,a^2\,b^5+4\,B\,a^3\,b^4+6\,B\,a^4\,b^3-B\,a^5\,b^2+6\,C\,a^2\,b^5+26\,C\,a^3\,b^4-11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,B\,a^6\,b-2\,C\,a\,b^6+4\,C\,a^6\,b\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6-7\,A\,a^3\,b^5+10\,A\,a^4\,b^4+36\,B\,a^2\,b^6-96\,B\,a^3\,b^5-14\,B\,a^4\,b^4+59\,B\,a^5\,b^3+3\,B\,a^6\,b^2-72\,C\,a^2\,b^6-60\,C\,a^3\,b^5+273\,C\,a^4\,b^4+47\,C\,a^5\,b^3-236\,C\,a^6\,b^2-18\,A\,a\,b^7-18\,B\,a^7\,b-12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6+7\,A\,a^3\,b^5+10\,A\,a^4\,b^4-36\,B\,a^2\,b^6-96\,B\,a^3\,b^5+14\,B\,a^4\,b^4+59\,B\,a^5\,b^3-3\,B\,a^6\,b^2-72\,C\,a^2\,b^6+60\,C\,a^3\,b^5+273\,C\,a^4\,b^4-47\,C\,a^5\,b^3-236\,C\,a^6\,b^2+18\,A\,a\,b^7-18\,B\,a^7\,b+12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a\,b^2-6\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3+6\,a^2\,b-2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3-6\,a^2\,b+2\,b^3\right)+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-4\,C\,a\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\left(B\,b-4\,C\,a\right)}{b^5}\right)\,\left(B\,b-4\,C\,a\right)\,1{}\mathrm{i}}{b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-4\,C\,a\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\left(B\,b-4\,C\,a\right)}{b^5}\right)\,\left(B\,b-4\,C\,a\right)\,1{}\mathrm{i}}{b^5}}{\frac{16\,\left(-9\,A^2\,B\,a^4\,b^{12}-12\,A^2\,B\,a^2\,b^{14}-4\,A^2\,B\,b^{16}+36\,A^2\,C\,a^5\,b^{11}+48\,A^2\,C\,a^3\,b^{13}+16\,A^2\,C\,a\,b^{15}-6\,A\,B^2\,a^9\,b^7-6\,A\,B^2\,a^8\,b^8+20\,A\,B^2\,a^7\,b^9+14\,A\,B^2\,a^6\,b^{10}-14\,A\,B^2\,a^5\,b^{11}-6\,A\,B^2\,a^4\,b^{12}+22\,A\,B^2\,a^3\,b^{13}-6\,A\,B^2\,a^2\,b^{14}+28\,A\,B^2\,a\,b^{15}+4\,A\,B^2\,b^{16}+48\,A\,B\,C\,a^{10}\,b^6+48\,A\,B\,C\,a^9\,b^7-160\,A\,B\,C\,a^8\,b^8-112\,A\,B\,C\,a^7\,b^9+130\,A\,B\,C\,a^6\,b^{10}+48\,A\,B\,C\,a^5\,b^{11}-92\,A\,B\,C\,a^4\,b^{12}+48\,A\,B\,C\,a^3\,b^{13}-176\,A\,B\,C\,a^2\,b^{14}-32\,A\,B\,C\,a\,b^{15}-96\,A\,C^2\,a^{11}\,b^5-96\,A\,C^2\,a^{10}\,b^6+320\,A\,C^2\,a^9\,b^7+224\,A\,C^2\,a^8\,b^8-296\,A\,C^2\,a^7\,b^9-96\,A\,C^2\,a^6\,b^{10}+16\,A\,C^2\,a^5\,b^{11}-96\,A\,C^2\,a^4\,b^{12}+256\,A\,C^2\,a^3\,b^{13}+64\,A\,C^2\,a^2\,b^{14}-4\,B^3\,a^{13}\,b^3+2\,B^3\,a^{12}\,b^4+26\,B^3\,a^{11}\,b^5-11\,B^3\,a^{10}\,b^6-70\,B^3\,a^9\,b^7+34\,B^3\,a^8\,b^8+110\,B^3\,a^7\,b^9-66\,B^3\,a^6\,b^{10}-110\,B^3\,a^5\,b^{11}+64\,B^3\,a^4\,b^{12}+64\,B^3\,a^3\,b^{13}-48\,B^3\,a^2\,b^{14}-16\,B^3\,a\,b^{15}+48\,B^2\,C\,a^{14}\,b^2-24\,B^2\,C\,a^{13}\,b^3-312\,B^2\,C\,a^{12}\,b^4+138\,B^2\,C\,a^{11}\,b^5+846\,B^2\,C\,a^{10}\,b^6-408\,B^2\,C\,a^9\,b^7-1314\,B^2\,C\,a^8\,b^8+726\,B^2\,C\,a^7\,b^9+1266\,B^2\,C\,a^6\,b^{10}-690\,B^2\,C\,a^5\,b^{11}-702\,B^2\,C\,a^4\,b^{12}+408\,B^2\,C\,a^3\,b^{13}+168\,B^2\,C\,a^2\,b^{14}-192\,B\,C^2\,a^{15}\,b+96\,B\,C^2\,a^{14}\,b^2+1248\,B\,C^2\,a^{13}\,b^3-576\,B\,C^2\,a^{12}\,b^4-3408\,B\,C^2\,a^{11}\,b^5+1632\,B\,C^2\,a^{10}\,b^6+5232\,B\,C^2\,a^9\,b^7-2649\,B\,C^2\,a^8\,b^8-4848\,B\,C^2\,a^7\,b^9+2376\,B\,C^2\,a^6\,b^{10}+2544\,B\,C^2\,a^5\,b^{11}-1104\,B\,C^2\,a^4\,b^{12}-576\,B\,C^2\,a^3\,b^{13}+256\,C^3\,a^{16}-128\,C^3\,a^{15}\,b-1664\,C^3\,a^{14}\,b^2+800\,C^3\,a^{13}\,b^3+4576\,C^3\,a^{12}\,b^4-2176\,C^3\,a^{11}\,b^5-6944\,C^3\,a^{10}\,b^6+3204\,C^3\,a^9\,b^7+6176\,C^3\,a^8\,b^8-2560\,C^3\,a^7\,b^9-3040\,C^3\,a^6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2\,a^5\,b^{11}-96\,A\,C^2\,a^4\,b^{12}+256\,A\,C^2\,a^3\,b^{13}+64\,A\,C^2\,a^2\,b^{14}-4\,B^3\,a^{13}\,b^3+2\,B^3\,a^{12}\,b^4+26\,B^3\,a^{11}\,b^5-11\,B^3\,a^{10}\,b^6-70\,B^3\,a^9\,b^7+34\,B^3\,a^8\,b^8+110\,B^3\,a^7\,b^9-66\,B^3\,a^6\,b^{10}-110\,B^3\,a^5\,b^{11}+64\,B^3\,a^4\,b^{12}+64\,B^3\,a^3\,b^{13}-48\,B^3\,a^2\,b^{14}-16\,B^3\,a\,b^{15}+48\,B^2\,C\,a^{14}\,b^2-24\,B^2\,C\,a^{13}\,b^3-312\,B^2\,C\,a^{12}\,b^4+138\,B^2\,C\,a^{11}\,b^5+846\,B^2\,C\,a^{10}\,b^6-408\,B^2\,C\,a^9\,b^7-1314\,B^2\,C\,a^8\,b^8+726\,B^2\,C\,a^7\,b^9+1266\,B^2\,C\,a^6\,b^{10}-690\,B^2\,C\,a^5\,b^{11}-702\,B^2\,C\,a^4\,b^{12}+408\,B^2\,C\,a^3\,b^{13}+168\,B^2\,C\,a^2\,b^{14}-192\,B\,C^2\,a^{15}\,b+96\,B\,C^2\,a^{14}\,b^2+1248\,B\,C^2\,a^{13}\,b^3-576\,B\,C^2\,a^{12}\,b^4-3408\,B\,C^2\,a^{11}\,b^5+1632\,B\,C^2\,a^{10}\,b^6+5232\,B\,C^2\,a^9\,b^7-2649\,B\,C^2\,a^8\,b^8-4848\,B\,C^2\,a^7\,b^9+2376\,B\,C^2\,a^6\,b^{10}+2544\,B\,C^2\,a^5\,b^{11}-1104\,B\,C^2\,a^4\,b^{12}-576\,B\,C^2\,a^3\,b^{13}+256\,C^3\,a^{16}-128\,C^3\,a^{15}\,b-1664\,C^3\,a^{14}\,b^2+800\,C^3\,a^{13}\,b^3+4576\,C^3\,a^{12}\,b^4-2176\,C^3\,a^{11}\,b^5-6944\,C^3\,a^{10}\,b^6+3204\,C^3\,a^9\,b^7+6176\,C^3\,a^8\,b^8-2560\,C^3\,a^7\,b^9-3040\,C^3\,a^6\,b^{10}+960\,C^3\,a^5\,b^{11}+640\,C^3\,a^4\,b^{12}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}","Not used",1,"(atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (8*tan(c/2 + (d*x)/2)*(B*b - 4*C*a)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(B*b - 4*C*a))/b^5)*(B*b - 4*C*a)*1i)/b^5 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (8*tan(c/2 + (d*x)/2)*(B*b - 4*C*a)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(B*b - 4*C*a))/b^5)*(B*b - 4*C*a)*1i)/b^5)/((16*(256*C^3*a^16 + 4*A*B^2*b^16 - 4*A^2*B*b^16 - 16*B^3*a*b^15 - 128*C^3*a^15*b - 48*B^3*a^2*b^14 + 64*B^3*a^3*b^13 + 64*B^3*a^4*b^12 - 110*B^3*a^5*b^11 - 66*B^3*a^6*b^10 + 110*B^3*a^7*b^9 + 34*B^3*a^8*b^8 - 70*B^3*a^9*b^7 - 11*B^3*a^10*b^6 + 26*B^3*a^11*b^5 + 2*B^3*a^12*b^4 - 4*B^3*a^13*b^3 + 640*C^3*a^4*b^12 + 960*C^3*a^5*b^11 - 3040*C^3*a^6*b^10 - 2560*C^3*a^7*b^9 + 6176*C^3*a^8*b^8 + 3204*C^3*a^9*b^7 - 6944*C^3*a^10*b^6 - 2176*C^3*a^11*b^5 + 4576*C^3*a^12*b^4 + 800*C^3*a^13*b^3 - 1664*C^3*a^14*b^2 + 28*A*B^2*a*b^15 + 16*A^2*C*a*b^15 - 192*B*C^2*a^15*b - 6*A*B^2*a^2*b^14 + 22*A*B^2*a^3*b^13 - 6*A*B^2*a^4*b^12 - 14*A*B^2*a^5*b^11 + 14*A*B^2*a^6*b^10 + 20*A*B^2*a^7*b^9 - 6*A*B^2*a^8*b^8 - 6*A*B^2*a^9*b^7 - 12*A^2*B*a^2*b^14 - 9*A^2*B*a^4*b^12 + 64*A*C^2*a^2*b^14 + 256*A*C^2*a^3*b^13 - 96*A*C^2*a^4*b^12 + 16*A*C^2*a^5*b^11 - 96*A*C^2*a^6*b^10 - 296*A*C^2*a^7*b^9 + 224*A*C^2*a^8*b^8 + 320*A*C^2*a^9*b^7 - 96*A*C^2*a^10*b^6 - 96*A*C^2*a^11*b^5 + 48*A^2*C*a^3*b^13 + 36*A^2*C*a^5*b^11 - 576*B*C^2*a^3*b^13 - 1104*B*C^2*a^4*b^12 + 2544*B*C^2*a^5*b^11 + 2376*B*C^2*a^6*b^10 - 4848*B*C^2*a^7*b^9 - 2649*B*C^2*a^8*b^8 + 5232*B*C^2*a^9*b^7 + 1632*B*C^2*a^10*b^6 - 3408*B*C^2*a^11*b^5 - 576*B*C^2*a^12*b^4 + 1248*B*C^2*a^13*b^3 + 96*B*C^2*a^14*b^2 + 168*B^2*C*a^2*b^14 + 408*B^2*C*a^3*b^13 - 702*B^2*C*a^4*b^12 - 690*B^2*C*a^5*b^11 + 1266*B^2*C*a^6*b^10 + 726*B^2*C*a^7*b^9 - 1314*B^2*C*a^8*b^8 - 408*B^2*C*a^9*b^7 + 846*B^2*C*a^10*b^6 + 138*B^2*C*a^11*b^5 - 312*B^2*C*a^12*b^4 - 24*B^2*C*a^13*b^3 + 48*B^2*C*a^14*b^2 - 32*A*B*C*a*b^15 - 176*A*B*C*a^2*b^14 + 48*A*B*C*a^3*b^13 - 92*A*B*C*a^4*b^12 + 48*A*B*C*a^5*b^11 + 130*A*B*C*a^6*b^10 - 112*A*B*C*a^7*b^9 - 160*A*B*C*a^8*b^8 + 48*A*B*C*a^9*b^7 + 48*A*B*C*a^10*b^6))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (8*tan(c/2 + (d*x)/2)*(B*b - 4*C*a)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(B*b - 4*C*a))/b^5)*(B*b - 4*C*a))/b^5 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (8*tan(c/2 + (d*x)/2)*(B*b - 4*C*a)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(B*b - 4*C*a))/b^5)*(B*b - 4*C*a))/b^5))*(B*b - 4*C*a)*2i)/(b^5*d) - ((tan(c/2 + (d*x)/2)^7*(8*C*a^7 + 2*C*b^7 + 3*A*a^2*b^5 + 2*A*a^3*b^4 - 12*B*a^2*b^5 - 4*B*a^3*b^4 + 6*B*a^4*b^3 + B*a^5*b^2 - 6*C*a^2*b^5 + 26*C*a^3*b^4 + 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*B*a^6*b - 2*C*a*b^6 - 4*C*a^6*b))/(b^4*(a + b)^3*(a - b)) - (tan(c/2 + (d*x)/2)*(8*C*a^7 - 2*C*b^7 - 3*A*a^2*b^5 + 2*A*a^3*b^4 - 12*B*a^2*b^5 + 4*B*a^3*b^4 + 6*B*a^4*b^3 - B*a^5*b^2 + 6*C*a^2*b^5 + 26*C*a^3*b^4 - 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*B*a^6*b - 2*C*a*b^6 + 4*C*a^6*b))/(b^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^3*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 - 7*A*a^3*b^5 + 10*A*a^4*b^4 + 36*B*a^2*b^6 - 96*B*a^3*b^5 - 14*B*a^4*b^4 + 59*B*a^5*b^3 + 3*B*a^6*b^2 - 72*C*a^2*b^6 - 60*C*a^3*b^5 + 273*C*a^4*b^4 + 47*C*a^5*b^3 - 236*C*a^6*b^2 - 18*A*a*b^7 - 18*B*a^7*b - 12*C*a^7*b))/(3*b^4*(a + b)^2*(a - b)^3) - (tan(c/2 + (d*x)/2)^5*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 + 7*A*a^3*b^5 + 10*A*a^4*b^4 - 36*B*a^2*b^6 - 96*B*a^3*b^5 + 14*B*a^4*b^4 + 59*B*a^5*b^3 - 3*B*a^6*b^2 - 72*C*a^2*b^6 + 60*C*a^3*b^5 + 273*C*a^4*b^4 - 47*C*a^5*b^3 - 236*C*a^6*b^2 + 18*A*a*b^7 - 18*B*a^7*b + 12*C*a^7*b))/(3*b^4*(a + b)^3*(a - b)^2))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^3) - tan(c/2 + (d*x)/2)^2*(6*a^2*b + 4*a^3 - 2*b^3) - tan(c/2 + (d*x)/2)^6*(4*a^3 - 6*a^2*b + 2*b^3) + a^3 + b^3 + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))/((16*(256*C^3*a^16 + 4*A*B^2*b^16 - 4*A^2*B*b^16 - 16*B^3*a*b^15 - 128*C^3*a^15*b - 48*B^3*a^2*b^14 + 64*B^3*a^3*b^13 + 64*B^3*a^4*b^12 - 110*B^3*a^5*b^11 - 66*B^3*a^6*b^10 + 110*B^3*a^7*b^9 + 34*B^3*a^8*b^8 - 70*B^3*a^9*b^7 - 11*B^3*a^10*b^6 + 26*B^3*a^11*b^5 + 2*B^3*a^12*b^4 - 4*B^3*a^13*b^3 + 640*C^3*a^4*b^12 + 960*C^3*a^5*b^11 - 3040*C^3*a^6*b^10 - 2560*C^3*a^7*b^9 + 6176*C^3*a^8*b^8 + 3204*C^3*a^9*b^7 - 6944*C^3*a^10*b^6 - 2176*C^3*a^11*b^5 + 4576*C^3*a^12*b^4 + 800*C^3*a^13*b^3 - 1664*C^3*a^14*b^2 + 28*A*B^2*a*b^15 + 16*A^2*C*a*b^15 - 192*B*C^2*a^15*b - 6*A*B^2*a^2*b^14 + 22*A*B^2*a^3*b^13 - 6*A*B^2*a^4*b^12 - 14*A*B^2*a^5*b^11 + 14*A*B^2*a^6*b^10 + 20*A*B^2*a^7*b^9 - 6*A*B^2*a^8*b^8 - 6*A*B^2*a^9*b^7 - 12*A^2*B*a^2*b^14 - 9*A^2*B*a^4*b^12 + 64*A*C^2*a^2*b^14 + 256*A*C^2*a^3*b^13 - 96*A*C^2*a^4*b^12 + 16*A*C^2*a^5*b^11 - 96*A*C^2*a^6*b^10 - 296*A*C^2*a^7*b^9 + 224*A*C^2*a^8*b^8 + 320*A*C^2*a^9*b^7 - 96*A*C^2*a^10*b^6 - 96*A*C^2*a^11*b^5 + 48*A^2*C*a^3*b^13 + 36*A^2*C*a^5*b^11 - 576*B*C^2*a^3*b^13 - 1104*B*C^2*a^4*b^12 + 2544*B*C^2*a^5*b^11 + 2376*B*C^2*a^6*b^10 - 4848*B*C^2*a^7*b^9 - 2649*B*C^2*a^8*b^8 + 5232*B*C^2*a^9*b^7 + 1632*B*C^2*a^10*b^6 - 3408*B*C^2*a^11*b^5 - 576*B*C^2*a^12*b^4 + 1248*B*C^2*a^13*b^3 + 96*B*C^2*a^14*b^2 + 168*B^2*C*a^2*b^14 + 408*B^2*C*a^3*b^13 - 702*B^2*C*a^4*b^12 - 690*B^2*C*a^5*b^11 + 1266*B^2*C*a^6*b^10 + 726*B^2*C*a^7*b^9 - 1314*B^2*C*a^8*b^8 - 408*B^2*C*a^9*b^7 + 846*B^2*C*a^10*b^6 + 138*B^2*C*a^11*b^5 - 312*B^2*C*a^12*b^4 - 24*B^2*C*a^13*b^3 + 48*B^2*C*a^14*b^2 - 32*A*B*C*a*b^15 - 176*A*B*C*a^2*b^14 + 48*A*B*C*a^3*b^13 - 92*A*B*C*a^4*b^12 + 48*A*B*C*a^5*b^11 + 130*A*B*C*a^6*b^10 - 112*A*B*C*a^7*b^9 - 160*A*B*C*a^8*b^8 + 48*A*B*C*a^9*b^7 + 48*A*B*C*a^10*b^6))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*1i)/(d*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))","B"
924,1,11926,358,19.092963,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^4),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4-A\,a^3\,b^3+3\,B\,a^2\,b^4-2\,B\,a^3\,b^3+12\,C\,a^2\,b^4-4\,C\,a^3\,b^3-6\,C\,a^4\,b^2-2\,A\,a\,b^5-6\,B\,a\,b^5+C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6+7\,A\,a^2\,b^4-B\,a^3\,b^3+18\,C\,a^2\,b^4-11\,C\,a^4\,b^2-9\,B\,a\,b^5\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4+A\,a^3\,b^3-3\,B\,a^2\,b^4-2\,B\,a^3\,b^3+12\,C\,a^2\,b^4+4\,C\,a^3\,b^3-6\,C\,a^4\,b^2+2\,A\,a\,b^5-6\,B\,a\,b^5-C\,a^5\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-6\,A\,B\,C\,a^5\,b^8-28\,A\,B\,C\,a^3\,b^{10}-16\,A\,B\,C\,a\,b^{12}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+9\,B^2\,C\,a^4\,b^9+12\,B^2\,C\,a^2\,b^{11}+4\,B^2\,C\,b^{13}+6\,B\,C^2\,a^9\,b^4+6\,B\,C^2\,a^8\,b^5-20\,B\,C^2\,a^7\,b^6-14\,B\,C^2\,a^6\,b^7+14\,B\,C^2\,a^5\,b^8+6\,B\,C^2\,a^4\,b^9-22\,B\,C^2\,a^3\,b^{10}+6\,B\,C^2\,a^2\,b^{11}-28\,B\,C^2\,a\,b^{12}-4\,B\,C^2\,b^{13}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)}{b^4}-\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{8\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)}{b^4}\right)}{b^4}}\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-6\,A\,B\,C\,a^5\,b^8-28\,A\,B\,C\,a^3\,b^{10}-16\,A\,B\,C\,a\,b^{12}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+9\,B^2\,C\,a^4\,b^9+12\,B^2\,C\,a^2\,b^{11}+4\,B^2\,C\,b^{13}+6\,B\,C^2\,a^9\,b^4+6\,B\,C^2\,a^8\,b^5-20\,B\,C^2\,a^7\,b^6-14\,B\,C^2\,a^6\,b^7+14\,B\,C^2\,a^5\,b^8+6\,B\,C^2\,a^4\,b^9-22\,B\,C^2\,a^3\,b^{10}+6\,B\,C^2\,a^2\,b^{11}-28\,B\,C^2\,a\,b^{12}-4\,B\,C^2\,b^{13}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 - A*a^3*b^3 + 3*B*a^2*b^4 - 2*B*a^3*b^3 + 12*C*a^2*b^4 - 4*C*a^3*b^3 - 6*C*a^4*b^2 - 2*A*a*b^5 - 6*B*a*b^5 + C*a^5*b))/((a + b)*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 + 7*A*a^2*b^4 - B*a^3*b^3 + 18*C*a^2*b^4 - 11*C*a^4*b^2 - 9*B*a*b^5))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*b^3)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 + A*a^3*b^3 - 3*B*a^2*b^4 - 2*B*a^3*b^3 + 12*C*a^2*b^4 + 4*C*a^3*b^3 - 6*C*a^4*b^2 + 2*A*a*b^5 - 6*B*a*b^5 - C*a^5*b))/((a*b^3 - b^4)*(a + b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (C*atan(((C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4)*1i)/b^4 + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4)*1i)/b^4)/((16*(4*C^3*a^13 - 4*B*C^2*b^13 + 4*B^2*C*b^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 - 28*B*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7 + 6*B*C^2*a^2*b^11 - 22*B*C^2*a^3*b^10 + 6*B*C^2*a^4*b^9 + 14*B*C^2*a^5*b^8 - 14*B*C^2*a^6*b^7 - 20*B*C^2*a^7*b^6 + 6*B*C^2*a^8*b^5 + 6*B*C^2*a^9*b^4 + 12*B^2*C*a^2*b^11 + 9*B^2*C*a^4*b^9 - 16*A*B*C*a*b^12 - 28*A*B*C*a^3*b^10 - 6*A*B*C*a^5*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4))/b^4 - (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (8*C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6))))/b^4))/b^4))*2i)/(b^4*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))/((16*(4*C^3*a^13 - 4*B*C^2*b^13 + 4*B^2*C*b^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 - 28*B*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7 + 6*B*C^2*a^2*b^11 - 22*B*C^2*a^3*b^10 + 6*B*C^2*a^4*b^9 + 14*B*C^2*a^5*b^8 - 14*B*C^2*a^6*b^7 - 20*B*C^2*a^7*b^6 + 6*B*C^2*a^8*b^5 + 6*B*C^2*a^9*b^4 + 12*B^2*C*a^2*b^11 + 9*B^2*C*a^4*b^9 - 16*A*B*C*a*b^12 - 28*A*B*C*a^3*b^10 - 6*A*B*C*a^5*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*1i)/(d*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))","B"
925,1,516,314,7.697935,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^4),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^3-A\,b^3+B\,a^3-2\,B\,b^3+2\,C\,a^3+6\,A\,a\,b^2-2\,A\,a^2\,b+2\,B\,a\,b^2-6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^3-3\,B\,b^3+C\,a^3+7\,A\,a\,b^2-7\,B\,a^2\,b+9\,C\,a\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^3+A\,b^3-B\,a^3-2\,B\,b^3+2\,C\,a^3+6\,A\,a\,b^2+2\,A\,a^2\,b-2\,B\,a\,b^2-6\,B\,a^2\,b+6\,C\,a\,b^2+3\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(A\,b^3-B\,a^3+2\,C\,b^3+4\,A\,a^2\,b-4\,B\,a\,b^2+3\,C\,a^2\,b\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^3 - A*b^3 + B*a^3 - 2*B*b^3 + 2*C*a^3 + 6*A*a*b^2 - 2*A*a^2*b + 2*B*a*b^2 - 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)) - (4*tan(c/2 + (d*x)/2)^3*(3*A*a^3 - 3*B*b^3 + C*a^3 + 7*A*a*b^2 - 7*B*a^2*b + 9*C*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*a^3 + A*b^3 - B*a^3 - 2*B*b^3 + 2*C*a^3 + 6*A*a*b^2 + 2*A*a^2*b - 2*B*a*b^2 - 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/((a + b)^3*(a - b)))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (atanh((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(a + b)^(1/2)*(a - b)^(7/2)))*(A*b^3 - B*a^3 + 2*C*b^3 + 4*A*a^2*b - 4*B*a*b^2 + 3*C*a^2*b))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
926,1,516,299,8.398453,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^4),x)","\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(2\,A\,a^3-B\,b^3+C\,a^3+3\,A\,a\,b^2-4\,B\,a^2\,b+4\,C\,a\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-2\,B\,a^3+B\,b^3-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2+2\,B\,a^2\,b-2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^3-3\,B\,a^3+3\,C\,b^3+9\,A\,a^2\,b-7\,B\,a\,b^2+7\,C\,a^2\,b\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^3-2\,B\,a^3-B\,b^3+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2-2\,B\,a^2\,b+2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(atanh((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(a + b)^(1/2)*(a - b)^(7/2)))*(2*A*a^3 - B*b^3 + C*a^3 + 3*A*a*b^2 - 4*B*a^2*b + 4*C*a*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((tan(c/2 + (d*x)/2)*(2*A*b^3 - 2*B*a^3 + B*b^3 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 + 2*B*a^2*b - 2*C*a*b^2 + 6*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)) - (4*tan(c/2 + (d*x)/2)^3*(A*b^3 - 3*B*a^3 + 3*C*b^3 + 9*A*a^2*b - 7*B*a*b^2 + 7*C*a^2*b))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^3 - 2*B*a^3 - B*b^3 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 - 2*B*a^2*b + 2*C*a*b^2 + 6*C*a^2*b))/((a + b)^3*(a - b)))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))","B"
927,1,11934,336,18.654810,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^4,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4-4\,A\,a^3\,b^3+12\,A\,a^4\,b^2-2\,B\,a^3\,b^3+3\,B\,a^4\,b^2-C\,a^3\,b^3+6\,C\,a^4\,b^2+A\,a\,b^5-6\,B\,a^5\,b-2\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6-11\,A\,a^2\,b^4+18\,A\,a^4\,b^2-B\,a^3\,b^3+7\,C\,a^4\,b^2-9\,B\,a^5\,b\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4+4\,A\,a^3\,b^3+12\,A\,a^4\,b^2-2\,B\,a^3\,b^3-3\,B\,a^4\,b^2+C\,a^3\,b^3+6\,C\,a^4\,b^2-A\,a\,b^5-6\,B\,a^5\,b+2\,C\,a^5\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{2\,A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)}{a^4}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)}{a^4}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}-4\,A^2\,B\,a^{13}-28\,A^2\,B\,a^{12}\,b+6\,A^2\,B\,a^{11}\,b^2-22\,A^2\,B\,a^{10}\,b^3+6\,A^2\,B\,a^9\,b^4+14\,A^2\,B\,a^8\,b^5-14\,A^2\,B\,a^7\,b^6-20\,A^2\,B\,a^6\,b^7+6\,A^2\,B\,a^5\,b^8+6\,A^2\,B\,a^4\,b^9+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4-16\,A\,B\,C\,a^{12}\,b-28\,A\,B\,C\,a^{10}\,b^3-6\,A\,B\,C\,a^8\,b^5+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,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,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}-4\,A^2\,B\,a^{13}-28\,A^2\,B\,a^{12}\,b+6\,A^2\,B\,a^{11}\,b^2-22\,A^2\,B\,a^{10}\,b^3+6\,A^2\,B\,a^9\,b^4+14\,A^2\,B\,a^8\,b^5-14\,A^2\,B\,a^7\,b^6-20\,A^2\,B\,a^6\,b^7+6\,A^2\,B\,a^5\,b^8+6\,A^2\,B\,a^4\,b^9+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4-16\,A\,B\,C\,a^{12}\,b-28\,A\,B\,C\,a^{10}\,b^3-6\,A\,B\,C\,a^8\,b^5+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}","Not used",1,"(2*A*atan(((A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4))/a^4 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4))/a^4)/((16*(4*A^3*b^13 + 4*A*B^2*a^13 - 4*A^2*B*a^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 - 28*A^2*B*a^12*b + 8*A^2*C*a^12*b + 9*A*B^2*a^9*b^4 + 12*A*B^2*a^11*b^2 + 6*A^2*B*a^4*b^9 + 6*A^2*B*a^5*b^8 - 20*A^2*B*a^6*b^7 - 14*A^2*B*a^7*b^6 + 14*A^2*B*a^8*b^5 + 6*A^2*B*a^9*b^4 - 22*A^2*B*a^10*b^3 + 6*A^2*B*a^11*b^2 + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2 - 16*A*B*C*a^12*b - 6*A*B*C*a^8*b^5 - 28*A*B*C*a^10*b^3))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4)*1i)/a^4 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2)*8i)/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*1i)/a^4)*1i)/a^4)))/(a^4*d) - ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 - 4*A*a^3*b^3 + 12*A*a^4*b^2 - 2*B*a^3*b^3 + 3*B*a^4*b^2 - C*a^3*b^3 + 6*C*a^4*b^2 + A*a*b^5 - 6*B*a^5*b - 2*C*a^5*b))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 - 11*A*a^2*b^4 + 18*A*a^4*b^2 - B*a^3*b^3 + 7*C*a^4*b^2 - 9*B*a^5*b))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 + 4*A*a^3*b^3 + 12*A*a^4*b^2 - 2*B*a^3*b^3 - 3*B*a^4*b^2 + C*a^3*b^3 + 6*C*a^4*b^2 - A*a*b^5 - 6*B*a^5*b + 2*C*a^5*b))/((a^3*b - a^4)*(a + b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/((16*(4*A^3*b^13 + 4*A*B^2*a^13 - 4*A^2*B*a^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 - 28*A^2*B*a^12*b + 8*A^2*C*a^12*b + 9*A*B^2*a^9*b^4 + 12*A*B^2*a^11*b^2 + 6*A^2*B*a^4*b^9 + 6*A^2*B*a^5*b^8 - 20*A^2*B*a^6*b^7 - 14*A^2*B*a^7*b^6 + 14*A^2*B*a^8*b^5 + 6*A^2*B*a^9*b^4 - 22*A^2*B*a^10*b^3 + 6*A^2*B*a^11*b^2 + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2 - 16*A*B*C*a^12*b - 6*A*B*C*a^8*b^5 - 28*A*B*C*a^10*b^3))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*1i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
928,1,9463,471,13.119297,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^7+8\,A\,b^7-24\,A\,a^2\,b^5+11\,A\,a^3\,b^4+26\,A\,a^4\,b^3-6\,A\,a^5\,b^2+B\,a^2\,b^5+6\,B\,a^3\,b^4-4\,B\,a^4\,b^3-12\,B\,a^5\,b^2+2\,C\,a^4\,b^3+3\,C\,a^5\,b^2-4\,A\,a\,b^6-2\,A\,a^6\,b-2\,B\,a\,b^6+6\,C\,a^6\,b\right)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^7-8\,A\,b^7+24\,A\,a^2\,b^5+11\,A\,a^3\,b^4-26\,A\,a^4\,b^3-6\,A\,a^5\,b^2+B\,a^2\,b^5-6\,B\,a^3\,b^4-4\,B\,a^4\,b^3+12\,B\,a^5\,b^2-2\,C\,a^4\,b^3+3\,C\,a^5\,b^2-4\,A\,a\,b^6+2\,A\,a^6\,b+2\,B\,a\,b^6-6\,C\,a^6\,b\right)}{\left(a+b\right)\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6+47\,A\,a^3\,b^5+273\,A\,a^4\,b^4-60\,A\,a^5\,b^3-72\,A\,a^6\,b^2+3\,B\,a^2\,b^6+59\,B\,a^3\,b^5-14\,B\,a^4\,b^4-96\,B\,a^5\,b^3+36\,B\,a^6\,b^2+10\,C\,a^4\,b^4-7\,C\,a^5\,b^3+45\,C\,a^6\,b^2-12\,A\,a\,b^7-18\,B\,a\,b^7-18\,C\,a^7\,b\right)}{3\,{\left(a+b\right)}^2\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6-47\,A\,a^3\,b^5+273\,A\,a^4\,b^4+60\,A\,a^5\,b^3-72\,A\,a^6\,b^2-3\,B\,a^2\,b^6+59\,B\,a^3\,b^5+14\,B\,a^4\,b^4-96\,B\,a^5\,b^3-36\,B\,a^6\,b^2+10\,C\,a^4\,b^4+7\,C\,a^5\,b^3+45\,C\,a^6\,b^2+12\,A\,a\,b^7-18\,B\,a\,b^7+18\,C\,a^7\,b\right)}{3\,\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2\,b-6\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^3+6\,a\,b^2+4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^3-6\,a\,b^2+4\,b^3\right)+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(4\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^5\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(A\,b\,4{}\mathrm{i}-B\,a\,1{}\mathrm{i}\right)}{a^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}{\frac{16\,\left(640\,A^3\,a^{12}\,b^4+960\,A^3\,a^{11}\,b^5-3040\,A^3\,a^{10}\,b^6-2560\,A^3\,a^9\,b^7+6176\,A^3\,a^8\,b^8+3204\,A^3\,a^7\,b^9-6944\,A^3\,a^6\,b^{10}-2176\,A^3\,a^5\,b^{11}+4576\,A^3\,a^4\,b^{12}+800\,A^3\,a^3\,b^{13}-1664\,A^3\,a^2\,b^{14}-128\,A^3\,a\,b^{15}+256\,A^3\,b^{16}-576\,A^2\,B\,a^{13}\,b^3-1104\,A^2\,B\,a^{12}\,b^4+2544\,A^2\,B\,a^{11}\,b^5+2376\,A^2\,B\,a^{10}\,b^6-4848\,A^2\,B\,a^9\,b^7-2649\,A^2\,B\,a^8\,b^8+5232\,A^2\,B\,a^7\,b^9+1632\,A^2\,B\,a^6\,b^{10}-3408\,A^2\,B\,a^5\,b^{11}-576\,A^2\,B\,a^4\,b^{12}+1248\,A^2\,B\,a^3\,b^{13}+96\,A^2\,B\,a^2\,b^{14}-192\,A^2\,B\,a\,b^{15}+64\,A^2\,C\,a^{14}\,b^2+256\,A^2\,C\,a^{13}\,b^3-96\,A^2\,C\,a^{12}\,b^4+16\,A^2\,C\,a^{11}\,b^5-96\,A^2\,C\,a^{10}\,b^6-296\,A^2\,C\,a^9\,b^7+224\,A^2\,C\,a^8\,b^8+320\,A^2\,C\,a^7\,b^9-96\,A^2\,C\,a^6\,b^{10}-96\,A^2\,C\,a^5\,b^{11}+168\,A\,B^2\,a^{14}\,b^2+408\,A\,B^2\,a^{13}\,b^3-702\,A\,B^2\,a^{12}\,b^4-690\,A\,B^2\,a^{11}\,b^5+1266\,A\,B^2\,a^{10}\,b^6+726\,A\,B^2\,a^9\,b^7-1314\,A\,B^2\,a^8\,b^8-408\,A\,B^2\,a^7\,b^9+846\,A\,B^2\,a^6\,b^{10}+138\,A\,B^2\,a^5\,b^{11}-312\,A\,B^2\,a^4\,b^{12}-24\,A\,B^2\,a^3\,b^{13}+48\,A\,B^2\,a^2\,b^{14}-32\,A\,B\,C\,a^{15}\,b-176\,A\,B\,C\,a^{14}\,b^2+48\,A\,B\,C\,a^{13}\,b^3-92\,A\,B\,C\,a^{12}\,b^4+48\,A\,B\,C\,a^{11}\,b^5+130\,A\,B\,C\,a^{10}\,b^6-112\,A\,B\,C\,a^9\,b^7-160\,A\,B\,C\,a^8\,b^8+48\,A\,B\,C\,a^7\,b^9+48\,A\,B\,C\,a^6\,b^{10}+16\,A\,C^2\,a^{15}\,b+48\,A\,C^2\,a^{13}\,b^3+36\,A\,C^2\,a^{11}\,b^5-16\,B^3\,a^{15}\,b-48\,B^3\,a^{14}\,b^2+64\,B^3\,a^{13}\,b^3+64\,B^3\,a^{12}\,b^4-110\,B^3\,a^{11}\,b^5-66\,B^3\,a^{10}\,b^6+110\,B^3\,a^9\,b^7+34\,B^3\,a^8\,b^8-70\,B^3\,a^7\,b^9-11\,B^3\,a^6\,b^{10}+26\,B^3\,a^5\,b^{11}+2\,B^3\,a^4\,b^{12}-4\,B^3\,a^3\,b^{13}+4\,B^2\,C\,a^{16}+28\,B^2\,C\,a^{15}\,b-6\,B^2\,C\,a^{14}\,b^2+22\,B^2\,C\,a^{13}\,b^3-6\,B^2\,C\,a^{12}\,b^4-14\,B^2\,C\,a^{11}\,b^5+14\,B^2\,C\,a^{10}\,b^6+20\,B^2\,C\,a^9\,b^7-6\,B^2\,C\,a^8\,b^8-6\,B^2\,C\,a^7\,b^9-4\,B\,C^2\,a^{16}-12\,B\,C^2\,a^{14}\,b^2-9\,B\,C^2\,a^{12}\,b^4\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^7*(2*A*a^7 + 8*A*b^7 - 24*A*a^2*b^5 + 11*A*a^3*b^4 + 26*A*a^4*b^3 - 6*A*a^5*b^2 + B*a^2*b^5 + 6*B*a^3*b^4 - 4*B*a^4*b^3 - 12*B*a^5*b^2 + 2*C*a^4*b^3 + 3*C*a^5*b^2 - 4*A*a*b^6 - 2*A*a^6*b - 2*B*a*b^6 + 6*C*a^6*b))/((a^4*b - a^5)*(a + b)^3) - (tan(c/2 + (d*x)/2)*(2*A*a^7 - 8*A*b^7 + 24*A*a^2*b^5 + 11*A*a^3*b^4 - 26*A*a^4*b^3 - 6*A*a^5*b^2 + B*a^2*b^5 - 6*B*a^3*b^4 - 4*B*a^4*b^3 + 12*B*a^5*b^2 - 2*C*a^4*b^3 + 3*C*a^5*b^2 - 4*A*a*b^6 + 2*A*a^6*b + 2*B*a*b^6 - 6*C*a^6*b))/((a + b)*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)) + (tan(c/2 + (d*x)/2)^3*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 + 47*A*a^3*b^5 + 273*A*a^4*b^4 - 60*A*a^5*b^3 - 72*A*a^6*b^2 + 3*B*a^2*b^6 + 59*B*a^3*b^5 - 14*B*a^4*b^4 - 96*B*a^5*b^3 + 36*B*a^6*b^2 + 10*C*a^4*b^4 - 7*C*a^5*b^3 + 45*C*a^6*b^2 - 12*A*a*b^7 - 18*B*a*b^7 - 18*C*a^7*b))/(3*(a + b)^2*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)) - (tan(c/2 + (d*x)/2)^5*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 - 47*A*a^3*b^5 + 273*A*a^4*b^4 + 60*A*a^5*b^3 - 72*A*a^6*b^2 - 3*B*a^2*b^6 + 59*B*a^3*b^5 + 14*B*a^4*b^4 - 96*B*a^5*b^3 - 36*B*a^6*b^2 + 10*C*a^4*b^4 + 7*C*a^5*b^3 + 45*C*a^6*b^2 + 12*A*a*b^7 - 18*B*a*b^7 + 18*C*a^7*b))/(3*(a^4*b - a^5)*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a^2*b - 6*b^3) + tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 2*a^3 + 4*b^3) + tan(c/2 + (d*x)/2)^6*(2*a^3 - 6*a*b^2 + 4*b^3) + a^3 + b^3 - tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (log(tan(c/2 + (d*x)/2) - 1i)*(4*A*b - B*a)*1i)/(a^5*d) - (log(tan(c/2 + (d*x)/2) + 1i)*(A*b*4i - B*a*1i))/(a^5*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))/((16*(256*A^3*b^16 - 4*B*C^2*a^16 + 4*B^2*C*a^16 - 128*A^3*a*b^15 - 16*B^3*a^15*b - 1664*A^3*a^2*b^14 + 800*A^3*a^3*b^13 + 4576*A^3*a^4*b^12 - 2176*A^3*a^5*b^11 - 6944*A^3*a^6*b^10 + 3204*A^3*a^7*b^9 + 6176*A^3*a^8*b^8 - 2560*A^3*a^9*b^7 - 3040*A^3*a^10*b^6 + 960*A^3*a^11*b^5 + 640*A^3*a^12*b^4 - 4*B^3*a^3*b^13 + 2*B^3*a^4*b^12 + 26*B^3*a^5*b^11 - 11*B^3*a^6*b^10 - 70*B^3*a^7*b^9 + 34*B^3*a^8*b^8 + 110*B^3*a^9*b^7 - 66*B^3*a^10*b^6 - 110*B^3*a^11*b^5 + 64*B^3*a^12*b^4 + 64*B^3*a^13*b^3 - 48*B^3*a^14*b^2 - 192*A^2*B*a*b^15 + 16*A*C^2*a^15*b + 28*B^2*C*a^15*b + 48*A*B^2*a^2*b^14 - 24*A*B^2*a^3*b^13 - 312*A*B^2*a^4*b^12 + 138*A*B^2*a^5*b^11 + 846*A*B^2*a^6*b^10 - 408*A*B^2*a^7*b^9 - 1314*A*B^2*a^8*b^8 + 726*A*B^2*a^9*b^7 + 1266*A*B^2*a^10*b^6 - 690*A*B^2*a^11*b^5 - 702*A*B^2*a^12*b^4 + 408*A*B^2*a^13*b^3 + 168*A*B^2*a^14*b^2 + 96*A^2*B*a^2*b^14 + 1248*A^2*B*a^3*b^13 - 576*A^2*B*a^4*b^12 - 3408*A^2*B*a^5*b^11 + 1632*A^2*B*a^6*b^10 + 5232*A^2*B*a^7*b^9 - 2649*A^2*B*a^8*b^8 - 4848*A^2*B*a^9*b^7 + 2376*A^2*B*a^10*b^6 + 2544*A^2*B*a^11*b^5 - 1104*A^2*B*a^12*b^4 - 576*A^2*B*a^13*b^3 + 36*A*C^2*a^11*b^5 + 48*A*C^2*a^13*b^3 - 96*A^2*C*a^5*b^11 - 96*A^2*C*a^6*b^10 + 320*A^2*C*a^7*b^9 + 224*A^2*C*a^8*b^8 - 296*A^2*C*a^9*b^7 - 96*A^2*C*a^10*b^6 + 16*A^2*C*a^11*b^5 - 96*A^2*C*a^12*b^4 + 256*A^2*C*a^13*b^3 + 64*A^2*C*a^14*b^2 - 9*B*C^2*a^12*b^4 - 12*B*C^2*a^14*b^2 - 6*B^2*C*a^7*b^9 - 6*B^2*C*a^8*b^8 + 20*B^2*C*a^9*b^7 + 14*B^2*C*a^10*b^6 - 14*B^2*C*a^11*b^5 - 6*B^2*C*a^12*b^4 + 22*B^2*C*a^13*b^3 - 6*B^2*C*a^14*b^2 - 32*A*B*C*a^15*b + 48*A*B*C*a^6*b^10 + 48*A*B*C*a^7*b^9 - 160*A*B*C*a^8*b^8 - 112*A*B*C*a^9*b^7 + 130*A*B*C*a^10*b^6 + 48*A*B*C*a^11*b^5 - 92*A*B*C*a^12*b^4 + 48*A*B*C*a^13*b^3 - 176*A*B*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) - (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*1i)/(d*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))","B"
929,1,21910,648,27.987600,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(A\,a^8+20\,A\,b^8-2\,B\,a^8-59\,A\,a^2\,b^6+27\,A\,a^3\,b^5+57\,A\,a^4\,b^4-21\,A\,a^5\,b^3-11\,A\,a^6\,b^2+4\,B\,a^2\,b^6+24\,B\,a^3\,b^5-11\,B\,a^4\,b^4-26\,B\,a^5\,b^3+6\,B\,a^6\,b^2+2\,C\,a^2\,b^6-C\,a^3\,b^5-6\,C\,a^4\,b^4+4\,C\,a^5\,b^3+12\,C\,a^6\,b^2-10\,A\,a\,b^7+7\,A\,a^7\,b-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{a^5\,{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,A\,a^9-120\,A\,b^9+6\,B\,a^9+364\,A\,a^2\,b^7+71\,A\,a^3\,b^6-369\,A\,a^4\,b^5-45\,A\,a^5\,b^4+111\,A\,a^6\,b^3+3\,A\,a^7\,b^2+12\,B\,a^2\,b^7-148\,B\,a^3\,b^6-29\,B\,a^4\,b^5+159\,B\,a^5\,b^4+18\,B\,a^6\,b^3-30\,B\,a^7\,b^2-12\,C\,a^2\,b^7-3\,C\,a^3\,b^6+37\,C\,a^4\,b^5+8\,C\,a^5\,b^4-60\,C\,a^6\,b^3-30\,A\,a\,b^8-21\,A\,a^8\,b+48\,B\,a\,b^8-6\,B\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,A\,a^9+120\,A\,b^9-6\,B\,a^9-364\,A\,a^2\,b^7+71\,A\,a^3\,b^6+369\,A\,a^4\,b^5-45\,A\,a^5\,b^4-111\,A\,a^6\,b^3+3\,A\,a^7\,b^2+12\,B\,a^2\,b^7+148\,B\,a^3\,b^6-29\,B\,a^4\,b^5-159\,B\,a^5\,b^4+18\,B\,a^6\,b^3+30\,B\,a^7\,b^2+12\,C\,a^2\,b^7-3\,C\,a^3\,b^6-37\,C\,a^4\,b^5+8\,C\,a^5\,b^4+60\,C\,a^6\,b^3-30\,A\,a\,b^8+21\,A\,a^8\,b-48\,B\,a\,b^8-6\,B\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^{10}+180\,A\,b^{10}-611\,A\,a^2\,b^8+740\,A\,a^4\,b^6-324\,A\,a^6\,b^4+36\,A\,a^8\,b^2+248\,B\,a^3\,b^7-320\,B\,a^5\,b^5+132\,B\,a^7\,b^3+18\,C\,a^2\,b^8-62\,C\,a^4\,b^6+110\,C\,a^6\,b^4-36\,C\,a^8\,b^2-72\,B\,a\,b^9-18\,B\,a^9\,b\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^8+20\,A\,b^8+2\,B\,a^8-59\,A\,a^2\,b^6-27\,A\,a^3\,b^5+57\,A\,a^4\,b^4+21\,A\,a^5\,b^3-11\,A\,a^6\,b^2-4\,B\,a^2\,b^6+24\,B\,a^3\,b^5+11\,B\,a^4\,b^4-26\,B\,a^5\,b^3-6\,B\,a^6\,b^2+2\,C\,a^2\,b^6+C\,a^3\,b^5-6\,C\,a^4\,b^4-4\,C\,a^5\,b^3+12\,C\,a^6\,b^2+10\,A\,a\,b^7-7\,A\,a^7\,b-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{a^5\,\left(a+b\right)\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^3+3\,a^2\,b+9\,a\,b^2+5\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^3-6\,a^2\,b+6\,a\,b^2+10\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-2\,a^3+6\,a^2\,b+6\,a\,b^2-10\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3+3\,a^2\,b-9\,a\,b^2+5\,b^3\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}-16\,A\,B\,a^{17}\,b+32\,A\,B\,a^{16}\,b^2-240\,A\,B\,a^{15}\,b^3+448\,A\,B\,a^{14}\,b^4-144\,A\,B\,a^{13}\,b^5-3360\,A\,B\,a^{12}\,b^6+3360\,A\,B\,a^{11}\,b^7+8960\,A\,B\,a^{10}\,b^8-9200\,A\,B\,a^9\,b^9-12320\,A\,B\,a^8\,b^{10}+12430\,A\,B\,a^7\,b^{11}+9408\,A\,B\,a^6\,b^{12}-9408\,A\,B\,a^5\,b^{13}-3808\,A\,B\,a^4\,b^{14}+3808\,A\,B\,a^3\,b^{15}+640\,A\,B\,a^2\,b^{16}-640\,A\,B\,a\,b^{17}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{19}\,b^8+348\,B\,a^{20}\,b^7+772\,B\,a^{21}\,b^6-292\,B\,a^{22}\,b^5-380\,B\,a^{23}\,b^4+144\,B\,a^{24}\,b^3+80\,B\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,B\,a^{26}\,b-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-4{}\mathrm{i}\,B\,a\,b+10{}\mathrm{i}\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-4{}\mathrm{i}\,B\,a\,b+10{}\mathrm{i}\,A\,b^2\right)}{a^6}\right)\,\left(\left(\frac{A\,1{}\mathrm{i}}{2}+C\,1{}\mathrm{i}\right)\,a^2-4{}\mathrm{i}\,B\,a\,b+10{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}-16\,A\,B\,a^{17}\,b+32\,A\,B\,a^{16}\,b^2-240\,A\,B\,a^{15}\,b^3+448\,A\,B\,a^{14}\,b^4-144\,A\,B\,a^{13}\,b^5-3360\,A\,B\,a^{12}\,b^6+3360\,A\,B\,a^{11}\,b^7+8960\,A\,B\,a^{10}\,b^8-9200\,A\,B\,a^9\,b^9-12320\,A\,B\,a^8\,b^{10}+12430\,A\,B\,a^7\,b^{11}+9408\,A\,B\,a^6\,b^{12}-9408\,A\,B\,a^5\,b^{13}-3808\,A\,B\,a^4\,b^{14}+3808\,A\,B\,a^3\,b^{15}+640\,A\,B\,a^2\,b^{16}-640\,A\,B\,a\,b^{17}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52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A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{19}\,b^8+348\,B\,a^{20}\,b^7+772\,B\,a^{21}\,b^6-292\,B\,a^{22}\,b^5-380\,B\,a^{23}\,b^4+144\,B\,a^{24}\,b^3+80\,B\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,B\,a^{26}\,b-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}-16\,A\,B\,a^{17}\,b+32\,A\,B\,a^{16}\,b^2-240\,A\,B\,a^{15}\,b^3+448\,A\,B\,a^{14}\,b^4-144\,A\,B\,a^{13}\,b^5-3360\,A\,B\,a^{12}\,b^6+3360\,A\,B\,a^{11}\,b^7+8960\,A\,B\,a^{10}\,b^8-9200\,A\,B\,a^9\,b^9-12320\,A\,B\,a^8\,b^{10}+12430\,A\,B\,a^7\,b^{11}+9408\,A\,B\,a^6\,b^{12}-9408\,A\,B\,a^5\,b^{13}-3808\,A\,B\,a^4\,b^{14}+3808\,A\,B\,a^3\,b^{15}+640\,A\,B\,a^2\,b^{16}-640\,A\,B\,a\,b^{17}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{19}\,b^8+348\,B\,a^{20}\,b^7+772\,B\,a^{21}\,b^6-292\,B\,a^{22}\,b^5-380\,B\,a^{23}\,b^4+144\,B\,a^{24}\,b^3+80\,B\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,B\,a^{26}\,b-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^9*(A*a^8 + 20*A*b^8 - 2*B*a^8 - 59*A*a^2*b^6 + 27*A*a^3*b^5 + 57*A*a^4*b^4 - 21*A*a^5*b^3 - 11*A*a^6*b^2 + 4*B*a^2*b^6 + 24*B*a^3*b^5 - 11*B*a^4*b^4 - 26*B*a^5*b^3 + 6*B*a^6*b^2 + 2*C*a^2*b^6 - C*a^3*b^5 - 6*C*a^4*b^4 + 4*C*a^5*b^3 + 12*C*a^6*b^2 - 10*A*a*b^7 + 7*A*a^7*b - 8*B*a*b^7 + 2*B*a^7*b))/(a^5*(a + b)^3*(a - b)) - (2*tan(c/2 + (d*x)/2)^3*(6*A*a^9 - 120*A*b^9 + 6*B*a^9 + 364*A*a^2*b^7 + 71*A*a^3*b^6 - 369*A*a^4*b^5 - 45*A*a^5*b^4 + 111*A*a^6*b^3 + 3*A*a^7*b^2 + 12*B*a^2*b^7 - 148*B*a^3*b^6 - 29*B*a^4*b^5 + 159*B*a^5*b^4 + 18*B*a^6*b^3 - 30*B*a^7*b^2 - 12*C*a^2*b^7 - 3*C*a^3*b^6 + 37*C*a^4*b^5 + 8*C*a^5*b^4 - 60*C*a^6*b^3 - 30*A*a*b^8 - 21*A*a^8*b + 48*B*a*b^8 - 6*B*a^8*b))/(3*a^5*(a + b)^2*(a - b)^3) - (2*tan(c/2 + (d*x)/2)^7*(6*A*a^9 + 120*A*b^9 - 6*B*a^9 - 364*A*a^2*b^7 + 71*A*a^3*b^6 + 369*A*a^4*b^5 - 45*A*a^5*b^4 - 111*A*a^6*b^3 + 3*A*a^7*b^2 + 12*B*a^2*b^7 + 148*B*a^3*b^6 - 29*B*a^4*b^5 - 159*B*a^5*b^4 + 18*B*a^6*b^3 + 30*B*a^7*b^2 + 12*C*a^2*b^7 - 3*C*a^3*b^6 - 37*C*a^4*b^5 + 8*C*a^5*b^4 + 60*C*a^6*b^3 - 30*A*a*b^8 + 21*A*a^8*b - 48*B*a*b^8 - 6*B*a^8*b))/(3*a^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(9*A*a^10 + 180*A*b^10 - 611*A*a^2*b^8 + 740*A*a^4*b^6 - 324*A*a^6*b^4 + 36*A*a^8*b^2 + 248*B*a^3*b^7 - 320*B*a^5*b^5 + 132*B*a^7*b^3 + 18*C*a^2*b^8 - 62*C*a^4*b^6 + 110*C*a^6*b^4 - 36*C*a^8*b^2 - 72*B*a*b^9 - 18*B*a^9*b))/(3*a^5*(a + b)^3*(a - b)^3) + (tan(c/2 + (d*x)/2)*(A*a^8 + 20*A*b^8 + 2*B*a^8 - 59*A*a^2*b^6 - 27*A*a^3*b^5 + 57*A*a^4*b^4 + 21*A*a^5*b^3 - 11*A*a^6*b^2 - 4*B*a^2*b^6 + 24*B*a^3*b^5 + 11*B*a^4*b^4 - 26*B*a^5*b^3 - 6*B*a^6*b^2 + 2*C*a^2*b^6 + C*a^3*b^5 - 6*C*a^4*b^4 - 4*C*a^5*b^3 + 12*C*a^6*b^2 + 10*A*a*b^7 - 7*A*a^7*b - 8*B*a*b^7 + 2*B*a^7*b))/(a^5*(a + b)*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(9*a*b^2 + 3*a^2*b - a^3 + 5*b^3) + tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 2*a^3 + 10*b^3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 2*a^3 - 10*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a^2*b - 9*a*b^2 + a^3 + 5*b^3))) + (atan(((((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i))/a^6)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*1i)/a^6 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i))/a^6)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*1i)/a^6)/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 - 512*B^3*a^3*b^16 + 256*B^3*a^4*b^15 + 3328*B^3*a^5*b^14 - 1600*B^3*a^6*b^13 - 9152*B^3*a^7*b^12 + 4352*B^3*a^8*b^11 + 13888*B^3*a^9*b^10 - 6408*B^3*a^10*b^9 - 12352*B^3*a^11*b^8 + 5120*B^3*a^12*b^7 + 6080*B^3*a^13*b^6 - 1920*B^3*a^14*b^5 - 1280*B^3*a^15*b^4 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 - 9600*A^2*B*a*b^18 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 3840*A*B^2*a^2*b^17 - 1920*A*B^2*a^3*b^16 - 24768*A*B^2*a^4*b^15 + 11904*A*B^2*a^5*b^14 + 67392*A*B^2*a^6*b^13 - 31680*A*B^2*a^7*b^12 - 100368*A*B^2*a^8*b^11 + 45148*A*B^2*a^9*b^10 + 86512*A*B^2*a^10*b^9 - 34567*A*B^2*a^11*b^8 - 40368*A*B^2*a^12*b^7 + 11960*A*B^2*a^13*b^6 + 7440*A*B^2*a^14*b^5 + 80*A*B^2*a^15*b^4 + 320*A*B^2*a^16*b^3 + 4800*A^2*B*a^2*b^17 + 61440*A^2*B*a^3*b^16 - 29520*A^2*B*a^4*b^15 - 165384*A^2*B*a^5*b^14 + 76812*A^2*B*a^6*b^13 + 241596*A^2*B*a^7*b^12 - 105755*A^2*B*a^8*b^11 - 201479*A^2*B*a^9*b^10 + 77359*A^2*B*a^10*b^9 + 88721*A^2*B*a^11*b^8 - 24711*A^2*B*a^12*b^7 - 13929*A^2*B*a^13*b^6 - 255*A^2*B*a^14*b^5 - 1345*A^2*B*a^15*b^4 + 20*A^2*B*a^16*b^3 - 20*A^2*B*a^17*b^2 + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2 - 96*B*C^2*a^5*b^14 + 48*B*C^2*a^6*b^13 + 624*B*C^2*a^7*b^12 - 276*B*C^2*a^8*b^11 - 1692*B*C^2*a^9*b^10 + 816*B*C^2*a^10*b^9 + 2628*B*C^2*a^11*b^8 - 1452*B*C^2*a^12*b^7 - 2532*B*C^2*a^13*b^6 + 1380*B*C^2*a^14*b^5 + 1404*B*C^2*a^15*b^4 - 816*B*C^2*a^16*b^3 - 336*B*C^2*a^17*b^2 + 384*B^2*C*a^4*b^15 - 192*B^2*C*a^5*b^14 - 2496*B^2*C*a^6*b^13 + 1152*B^2*C*a^7*b^12 + 6816*B^2*C*a^8*b^11 - 3264*B^2*C*a^9*b^10 - 10464*B^2*C*a^10*b^9 + 5298*B^2*C*a^11*b^8 + 9696*B^2*C*a^12*b^7 - 4752*B^2*C*a^13*b^6 - 5088*B^2*C*a^14*b^5 + 2208*B^2*C*a^15*b^4 + 1152*B^2*C*a^16*b^3 - 1920*A*B*C*a^3*b^16 + 960*A*B*C*a^4*b^15 + 12384*A*B*C*a^5*b^14 - 5712*A*B*C*a^6*b^13 - 33456*A*B*C*a^7*b^12 + 15852*A*B*C*a^8*b^11 + 50436*A*B*C*a^9*b^10 - 25034*A*B*C*a^10*b^9 - 45404*A*B*C*a^11*b^8 + 21788*A*B*C*a^12*b^7 + 22716*A*B*C*a^13*b^6 - 9292*A*B*C*a^14*b^5 - 4548*A*B*C*a^15*b^4 - 112*A*B*C*a^16*b^3 - 208*A*B*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i))/a^6)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i))/a^6 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i))/a^6)*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i))/a^6))*(A*b^2*10i + a^2*((A*1i)/2 + C*1i) - B*a*b*4i)*2i)/(a^6*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 - 512*B^3*a^3*b^16 + 256*B^3*a^4*b^15 + 3328*B^3*a^5*b^14 - 1600*B^3*a^6*b^13 - 9152*B^3*a^7*b^12 + 4352*B^3*a^8*b^11 + 13888*B^3*a^9*b^10 - 6408*B^3*a^10*b^9 - 12352*B^3*a^11*b^8 + 5120*B^3*a^12*b^7 + 6080*B^3*a^13*b^6 - 1920*B^3*a^14*b^5 - 1280*B^3*a^15*b^4 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 - 9600*A^2*B*a*b^18 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 3840*A*B^2*a^2*b^17 - 1920*A*B^2*a^3*b^16 - 24768*A*B^2*a^4*b^15 + 11904*A*B^2*a^5*b^14 + 67392*A*B^2*a^6*b^13 - 31680*A*B^2*a^7*b^12 - 100368*A*B^2*a^8*b^11 + 45148*A*B^2*a^9*b^10 + 86512*A*B^2*a^10*b^9 - 34567*A*B^2*a^11*b^8 - 40368*A*B^2*a^12*b^7 + 11960*A*B^2*a^13*b^6 + 7440*A*B^2*a^14*b^5 + 80*A*B^2*a^15*b^4 + 320*A*B^2*a^16*b^3 + 4800*A^2*B*a^2*b^17 + 61440*A^2*B*a^3*b^16 - 29520*A^2*B*a^4*b^15 - 165384*A^2*B*a^5*b^14 + 76812*A^2*B*a^6*b^13 + 241596*A^2*B*a^7*b^12 - 105755*A^2*B*a^8*b^11 - 201479*A^2*B*a^9*b^10 + 77359*A^2*B*a^10*b^9 + 88721*A^2*B*a^11*b^8 - 24711*A^2*B*a^12*b^7 - 13929*A^2*B*a^13*b^6 - 255*A^2*B*a^14*b^5 - 1345*A^2*B*a^15*b^4 + 20*A^2*B*a^16*b^3 - 20*A^2*B*a^17*b^2 + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2 - 96*B*C^2*a^5*b^14 + 48*B*C^2*a^6*b^13 + 624*B*C^2*a^7*b^12 - 276*B*C^2*a^8*b^11 - 1692*B*C^2*a^9*b^10 + 816*B*C^2*a^10*b^9 + 2628*B*C^2*a^11*b^8 - 1452*B*C^2*a^12*b^7 - 2532*B*C^2*a^13*b^6 + 1380*B*C^2*a^14*b^5 + 1404*B*C^2*a^15*b^4 - 816*B*C^2*a^16*b^3 - 336*B*C^2*a^17*b^2 + 384*B^2*C*a^4*b^15 - 192*B^2*C*a^5*b^14 - 2496*B^2*C*a^6*b^13 + 1152*B^2*C*a^7*b^12 + 6816*B^2*C*a^8*b^11 - 3264*B^2*C*a^9*b^10 - 10464*B^2*C*a^10*b^9 + 5298*B^2*C*a^11*b^8 + 9696*B^2*C*a^12*b^7 - 4752*B^2*C*a^13*b^6 - 5088*B^2*C*a^14*b^5 + 2208*B^2*C*a^15*b^4 + 1152*B^2*C*a^16*b^3 - 1920*A*B*C*a^3*b^16 + 960*A*B*C*a^4*b^15 + 12384*A*B*C*a^5*b^14 - 5712*A*B*C*a^6*b^13 - 33456*A*B*C*a^7*b^12 + 15852*A*B*C*a^8*b^11 + 50436*A*B*C*a^9*b^10 - 25034*A*B*C*a^10*b^9 - 45404*A*B*C*a^11*b^8 + 21788*A*B*C*a^12*b^7 + 22716*A*B*C*a^13*b^6 - 9292*A*B*C*a^14*b^5 - 4548*A*B*C*a^15*b^4 - 112*A*B*C*a^16*b^3 - 208*A*B*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*1i)/(d*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))","B"
930,1,258,24,4.216517,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x)),x)","\frac{2\,C\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^2-2\,B\,C\,a\,b+C^2\,a^2+C^2\,b^2\right)}\right)}{d}-\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^2-2\,B\,C\,a\,b+C^2\,a^2+C^2\,b^2\right)}\right)}{d}","Not used",1,"(2*C*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b*atan((B^2*b^2*sin(c/2 + (d*x)/2) + C^2*a^2*sin(c/2 + (d*x)/2) + C^2*b^2*sin(c/2 + (d*x)/2) - 2*B*C*a*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(B^2*b^2 + C^2*a^2 + C^2*b^2 - 2*B*C*a*b))))/d - (2*C*a*atan((B^2*b^2*sin(c/2 + (d*x)/2) + C^2*a^2*sin(c/2 + (d*x)/2) + C^2*b^2*sin(c/2 + (d*x)/2) - 2*B*C*a*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(B^2*b^2 + C^2*a^2 + C^2*b^2 - 2*B*C*a*b))))/d","B"
931,1,1169,75,7.944601,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^2,x)","\frac{2\,C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^3+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^2}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a\,b^2-2\,B\,C\,a^2\,b-2\,B\,C\,b^3+C^2\,a^3+3\,C^2\,a\,b^2\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^3+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^2}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a\,b^2-2\,B\,C\,a^2\,b-2\,B\,C\,b^3+C^2\,a^3+3\,C^2\,a\,b^2\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{2\,C\,b^3\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{2\,B\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^3+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^2}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a\,b^2-2\,B\,C\,a^2\,b-2\,B\,C\,b^3+C^2\,a^3+3\,C^2\,a\,b^2\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{B\,a\,b^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{2\,C\,a^2\,b\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,{\left(a^2-b^2\right)}^{3/2}}+\frac{B\,b^4\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d\,{\left(a^2-b^2\right)}^{3/2}}-\frac{2\,B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^2-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b-2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^3+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^2}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a\,b^2-2\,B\,C\,a^2\,b-2\,B\,C\,b^3+C^2\,a^3+3\,C^2\,a\,b^2\right)}\right)}{a\,d\,\left(a^2-b^2\right)}-\frac{2\,C\,b\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{d\,\left(a^2-b^2\right)}+\frac{B\,b^2\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}}{a\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*C*b^2*atan((C^2*a^4*sin(c/2 + (d*x)/2) + B^2*a^2*b^2*sin(c/2 + (d*x)/2) + 3*C^2*a^2*b^2*sin(c/2 + (d*x)/2) - 2*B*C*a*b^3*sin(c/2 + (d*x)/2) - 2*B*C*a^3*b*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(C^2*a^3 + B^2*a*b^2 + 3*C^2*a*b^2 - 2*B*C*b^3 - 2*B*C*a^2*b))))/(d*(a^2 - b^2)) - (2*C*a^2*atan((C^2*a^4*sin(c/2 + (d*x)/2) + B^2*a^2*b^2*sin(c/2 + (d*x)/2) + 3*C^2*a^2*b^2*sin(c/2 + (d*x)/2) - 2*B*C*a*b^3*sin(c/2 + (d*x)/2) - 2*B*C*a^3*b*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(C^2*a^3 + B^2*a*b^2 + 3*C^2*a*b^2 - 2*B*C*b^3 - 2*B*C*a^2*b))))/(d*(a^2 - b^2)) - (2*C*b^3*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (2*B*a*b*atan((C^2*a^4*sin(c/2 + (d*x)/2) + B^2*a^2*b^2*sin(c/2 + (d*x)/2) + 3*C^2*a^2*b^2*sin(c/2 + (d*x)/2) - 2*B*C*a*b^3*sin(c/2 + (d*x)/2) - 2*B*C*a^3*b*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(C^2*a^3 + B^2*a*b^2 + 3*C^2*a*b^2 - 2*B*C*b^3 - 2*B*C*a^2*b))))/(d*(a^2 - b^2)) - (B*a*b^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (2*C*a^2*b*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)^(3/2)) + (B*b^4*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2)))/(a*d*(a^2 - b^2)^(3/2)) - (2*B*b^3*atan((C^2*a^4*sin(c/2 + (d*x)/2) + B^2*a^2*b^2*sin(c/2 + (d*x)/2) + 3*C^2*a^2*b^2*sin(c/2 + (d*x)/2) - 2*B*C*a*b^3*sin(c/2 + (d*x)/2) - 2*B*C*a^3*b*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(C^2*a^3 + B^2*a*b^2 + 3*C^2*a*b^2 - 2*B*C*b^3 - 2*B*C*a^2*b))))/(a*d*(a^2 - b^2)) - (2*C*b*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(d*(a^2 - b^2)) + (B*b^2*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/cos(c/2 + (d*x)/2))*((a + b)*(a - b))^(1/2))/(a*d*(a^2 - b^2))","B"
932,1,5260,140,12.863055,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^3,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^2}\right)\,\left(B\,b-C\,a\right)}{a^2}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^2}\right)\,\left(B\,b-C\,a\right)}{a^2}}{\frac{64\,\left(2\,B^3\,a^4\,b^4+2\,B^3\,a^3\,b^5-3\,B^3\,a^2\,b^6-B^3\,a\,b^7+B^3\,b^8-7\,B^2\,C\,a^5\,b^3-9\,B^2\,C\,a^4\,b^4+10\,B^2\,C\,a^3\,b^5+4\,B^2\,C\,a^2\,b^6-3\,B^2\,C\,a\,b^7+8\,B\,C^2\,a^6\,b^2+13\,B\,C^2\,a^5\,b^3-11\,B\,C^2\,a^4\,b^4-5\,B\,C^2\,a^3\,b^5+3\,B\,C^2\,a^2\,b^6-3\,C^3\,a^7\,b-6\,C^3\,a^6\,b^2+4\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^2}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^2}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^2}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^2}}\right)\,\left(B\,b-C\,a\right)}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^3-2\,C\,a\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,B^3\,a^4\,b^4+2\,B^3\,a^3\,b^5-3\,B^3\,a^2\,b^6-B^3\,a\,b^7+B^3\,b^8-7\,B^2\,C\,a^5\,b^3-9\,B^2\,C\,a^4\,b^4+10\,B^2\,C\,a^3\,b^5+4\,B^2\,C\,a^2\,b^6-3\,B^2\,C\,a\,b^7+8\,B\,C^2\,a^6\,b^2+13\,B\,C^2\,a^5\,b^3-11\,B\,C^2\,a^4\,b^4-5\,B\,C^2\,a^3\,b^5+3\,B\,C^2\,a^2\,b^6-3\,C^3\,a^7\,b-6\,C^3\,a^6\,b^2+4\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3+3\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5-5\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+2\,B^2\,b^8-2\,B\,C\,a^7\,b+4\,B\,C\,a^6\,b^2-10\,B\,C\,a^5\,b^3-8\,B\,C\,a^4\,b^4+12\,B\,C\,a^3\,b^5+4\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+8\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-7\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(\frac{32\,\left(C\,a^{10}+B\,a^4\,b^6-3\,B\,a^6\,b^4+B\,a^7\,b^3+2\,B\,a^8\,b^2-C\,a^5\,b^5-C\,a^6\,b^4+4\,C\,a^7\,b^3-B\,a^9\,b-3\,C\,a^9\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-C\,a\,b^2+B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"(2*atan(((((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*(B*b - C*a)*1i)/a^2)*(B*b - C*a))/a^2 + (((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*(B*b - C*a)*1i)/a^2)*(B*b - C*a))/a^2)/((64*(B^3*b^8 - B^3*a*b^7 - 3*C^3*a^7*b - 3*B^3*a^2*b^6 + 2*B^3*a^3*b^5 + 2*B^3*a^4*b^4 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 + 4*C^3*a^5*b^3 - 6*C^3*a^6*b^2 - 3*B^2*C*a*b^7 + 3*B*C^2*a^2*b^6 - 5*B*C^2*a^3*b^5 - 11*B*C^2*a^4*b^4 + 13*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 4*B^2*C*a^2*b^6 + 10*B^2*C*a^3*b^5 - 9*B^2*C*a^4*b^4 - 7*B^2*C*a^5*b^3))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*(B*b - C*a)*1i)/a^2)*(B*b - C*a)*1i)/a^2 - (((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (tan(c/2 + (d*x)/2)*(B*b - C*a)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*(B*b - C*a)*1i)/a^2)*(B*b - C*a)*1i)/a^2))*(B*b - C*a))/(a^2*d) - (2*tan(c/2 + (d*x)/2)*(B*b^3 - 2*C*a*b^2))/(d*(a + b)*(a*b - a^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b))) + (b*atan(((b*((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(B^3*b^8 - B^3*a*b^7 - 3*C^3*a^7*b - 3*B^3*a^2*b^6 + 2*B^3*a^3*b^5 + 2*B^3*a^4*b^4 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 + 4*C^3*a^5*b^3 - 6*C^3*a^6*b^2 - 3*B^2*C*a*b^7 + 3*B*C^2*a^2*b^6 - 5*B*C^2*a^3*b^5 - 11*B*C^2*a^4*b^4 + 13*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 4*B^2*C*a^2*b^6 + 10*B^2*C*a^3*b^5 - 9*B^2*C*a^4*b^4 - 7*B^2*C*a^5*b^3))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) - (b*((32*tan(c/2 + (d*x)/2)*(2*B^2*b^8 + C^2*a^8 - 2*B^2*a*b^7 - 2*C^2*a^7*b - 5*B^2*a^2*b^6 + 4*B^2*a^3*b^5 + 3*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 7*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 8*C^2*a^6*b^2 - 4*B*C*a*b^7 - 2*B*C*a^7*b + 4*B*C*a^2*b^6 + 12*B*C*a^3*b^5 - 8*B*C*a^4*b^4 - 10*B*C*a^5*b^3 + 4*B*C*a^6*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*((32*(C*a^10 + B*a^4*b^6 - 3*B*a^6*b^4 + B*a^7*b^3 + 2*B*a^8*b^2 - C*a^5*b^5 - C*a^6*b^4 + 4*C*a^7*b^3 - B*a^9*b - 3*C*a^9*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + 3*C*a^3 - 2*B*a^2*b - C*a*b^2)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))","B"
933,1,5322,231,11.823971,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^4,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b^5-6\,B\,a^2\,b^3+2\,C\,a^2\,b^3+10\,C\,a^3\,b^2-B\,a\,b^4-2\,C\,a\,b^4\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^5-6\,B\,a^2\,b^3-2\,C\,a^2\,b^3+10\,C\,a^3\,b^2+B\,a\,b^4-2\,C\,a\,b^4\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,1{}\mathrm{i}\right)}{a^3\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3+24\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5-52\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7+57\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9-32\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+8\,B^2\,b^{12}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-64\,B\,C\,a^8\,b^4+112\,B\,C\,a^7\,b^5+96\,B\,C\,a^6\,b^6-112\,B\,C\,a^5\,b^7-64\,B\,C\,a^4\,b^8+60\,B\,C\,a^3\,b^9+16\,B\,C\,a^2\,b^{10}-16\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+52\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-56\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+56\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(2\,B\,a^7\,b^9-4\,B\,a^6\,b^{10}-4\,C\,a^{16}+18\,B\,a^8\,b^8-4\,B\,a^9\,b^7-36\,B\,a^{10}\,b^6+6\,B\,a^{11}\,b^5+34\,B\,a^{12}\,b^4-8\,B\,a^{13}\,b^3-12\,B\,a^{14}\,b^2+4\,C\,a^7\,b^9-4\,C\,a^8\,b^8-16\,C\,a^9\,b^7+4\,C\,a^{10}\,b^6+36\,C\,a^{11}\,b^5-40\,C\,a^{13}\,b^3+4\,C\,a^{14}\,b^2+4\,B\,a^{15}\,b+16\,C\,a^{15}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3+24\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5-52\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7+57\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9-32\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+8\,B^2\,b^{12}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-64\,B\,C\,a^8\,b^4+112\,B\,C\,a^7\,b^5+96\,B\,C\,a^6\,b^6-112\,B\,C\,a^5\,b^7-64\,B\,C\,a^4\,b^8+60\,B\,C\,a^3\,b^9+16\,B\,C\,a^2\,b^{10}-16\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+52\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-56\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+56\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(2\,B\,a^7\,b^9-4\,B\,a^6\,b^{10}-4\,C\,a^{16}+18\,B\,a^8\,b^8-4\,B\,a^9\,b^7-36\,B\,a^{10}\,b^6+6\,B\,a^{11}\,b^5+34\,B\,a^{12}\,b^4-8\,B\,a^{13}\,b^3-12\,B\,a^{14}\,b^2+4\,C\,a^7\,b^9-4\,C\,a^8\,b^8-16\,C\,a^9\,b^7+4\,C\,a^{10}\,b^6+36\,C\,a^{11}\,b^5-40\,C\,a^{13}\,b^3+4\,C\,a^{14}\,b^2+4\,B\,a^{15}\,b+16\,C\,a^{15}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(-12\,B^3\,a^8\,b^4-24\,B^3\,a^7\,b^5+34\,B^3\,a^6\,b^6+26\,B^3\,a^5\,b^7-36\,B^3\,a^4\,b^8-13\,B^3\,a^3\,b^9+18\,B^3\,a^2\,b^{10}+2\,B^3\,a\,b^{11}-4\,B^3\,b^{12}+40\,B^2\,C\,a^9\,b^3+92\,B^2\,C\,a^8\,b^4-108\,B^2\,C\,a^7\,b^5-80\,B^2\,C\,a^6\,b^6+108\,B^2\,C\,a^5\,b^7+37\,B^2\,C\,a^4\,b^8-52\,B^2\,C\,a^3\,b^9-4\,B^2\,C\,a^2\,b^{10}+12\,B^2\,C\,a\,b^{11}-44\,B\,C^2\,a^{10}\,b^2-116\,B\,C^2\,a^9\,b^3+114\,B\,C^2\,a^8\,b^4+78\,B\,C^2\,a^7\,b^5-108\,B\,C^2\,a^6\,b^6-36\,B\,C^2\,a^5\,b^7+50\,B\,C^2\,a^4\,b^8+2\,B\,C^2\,a^3\,b^9-12\,B\,C^2\,a^2\,b^{10}+16\,C^3\,a^{11}\,b+48\,C^3\,a^{10}\,b^2-40\,C^3\,a^9\,b^3-24\,C^3\,a^8\,b^4+36\,C^3\,a^7\,b^5+12\,C^3\,a^6\,b^6-16\,C^3\,a^5\,b^7+4\,C^3\,a^3\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3+24\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5-52\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7+57\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9-32\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+8\,B^2\,b^{12}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-64\,B\,C\,a^8\,b^4+112\,B\,C\,a^7\,b^5+96\,B\,C\,a^6\,b^6-112\,B\,C\,a^5\,b^7-64\,B\,C\,a^4\,b^8+60\,B\,C\,a^3\,b^9+16\,B\,C\,a^2\,b^{10}-16\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+52\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-56\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+56\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(2\,B\,a^7\,b^9-4\,B\,a^6\,b^{10}-4\,C\,a^{16}+18\,B\,a^8\,b^8-4\,B\,a^9\,b^7-36\,B\,a^{10}\,b^6+6\,B\,a^{11}\,b^5+34\,B\,a^{12}\,b^4-8\,B\,a^{13}\,b^3-12\,B\,a^{14}\,b^2+4\,C\,a^7\,b^9-4\,C\,a^8\,b^8-16\,C\,a^9\,b^7+4\,C\,a^{10}\,b^6+36\,C\,a^{11}\,b^5-40\,C\,a^{13}\,b^3+4\,C\,a^{14}\,b^2+4\,B\,a^{15}\,b+16\,C\,a^{15}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3+24\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5-52\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7+57\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9-32\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+8\,B^2\,b^{12}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-64\,B\,C\,a^8\,b^4+112\,B\,C\,a^7\,b^5+96\,B\,C\,a^6\,b^6-112\,B\,C\,a^5\,b^7-64\,B\,C\,a^4\,b^8+60\,B\,C\,a^3\,b^9+16\,B\,C\,a^2\,b^{10}-16\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+52\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-56\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+56\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(2\,B\,a^7\,b^9-4\,B\,a^6\,b^{10}-4\,C\,a^{16}+18\,B\,a^8\,b^8-4\,B\,a^9\,b^7-36\,B\,a^{10}\,b^6+6\,B\,a^{11}\,b^5+34\,B\,a^{12}\,b^4-8\,B\,a^{13}\,b^3-12\,B\,a^{14}\,b^2+4\,C\,a^7\,b^9-4\,C\,a^8\,b^8-16\,C\,a^9\,b^7+4\,C\,a^{10}\,b^6+36\,C\,a^{11}\,b^5-40\,C\,a^{13}\,b^3+4\,C\,a^{14}\,b^2+4\,B\,a^{15}\,b+16\,C\,a^{15}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-8\,C\,a^5+6\,B\,a^4\,b+4\,C\,a^3\,b^2-5\,B\,a^2\,b^3-2\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1i)*(B*b - C*a)*1i)/(a^3*d) - ((tan(c/2 + (d*x)/2)^3*(2*B*b^5 - 6*B*a^2*b^3 + 2*C*a^2*b^3 + 10*C*a^3*b^2 - B*a*b^4 - 2*C*a*b^4))/((a^2*b - a^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*b^5 - 6*B*a^2*b^3 - 2*C*a^2*b^3 + 10*C*a^3*b^2 + B*a*b^4 - 2*C*a*b^4))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*1i))/(a^3*d) - (b*atan(((b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^12 + 4*C^2*a^12 - 8*B^2*a*b^11 - 8*C^2*a^11*b - 32*B^2*a^2*b^10 + 32*B^2*a^3*b^9 + 57*B^2*a^4*b^8 - 48*B^2*a^5*b^7 - 52*B^2*a^6*b^6 + 32*B^2*a^7*b^5 + 24*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 4*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 28*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 56*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 56*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 52*C^2*a^10*b^2 - 16*B*C*a*b^11 - 8*B*C*a^11*b + 16*B*C*a^2*b^10 + 60*B*C*a^3*b^9 - 64*B*C*a^4*b^8 - 112*B*C*a^5*b^7 + 96*B*C*a^6*b^6 + 112*B*C*a^7*b^5 - 64*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(2*B*a^7*b^9 - 4*B*a^6*b^10 - 4*C*a^16 + 18*B*a^8*b^8 - 4*B*a^9*b^7 - 36*B*a^10*b^6 + 6*B*a^11*b^5 + 34*B*a^12*b^4 - 8*B*a^13*b^3 - 12*B*a^14*b^2 + 4*C*a^7*b^9 - 4*C*a^8*b^8 - 16*C*a^9*b^7 + 4*C*a^10*b^6 + 36*C*a^11*b^5 - 40*C*a^13*b^3 + 4*C*a^14*b^2 + 4*B*a^15*b + 16*C*a^15*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^12 + 4*C^2*a^12 - 8*B^2*a*b^11 - 8*C^2*a^11*b - 32*B^2*a^2*b^10 + 32*B^2*a^3*b^9 + 57*B^2*a^4*b^8 - 48*B^2*a^5*b^7 - 52*B^2*a^6*b^6 + 32*B^2*a^7*b^5 + 24*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 4*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 28*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 56*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 56*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 52*C^2*a^10*b^2 - 16*B*C*a*b^11 - 8*B*C*a^11*b + 16*B*C*a^2*b^10 + 60*B*C*a^3*b^9 - 64*B*C*a^4*b^8 - 112*B*C*a^5*b^7 + 96*B*C*a^6*b^6 + 112*B*C*a^7*b^5 - 64*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(2*B*a^7*b^9 - 4*B*a^6*b^10 - 4*C*a^16 + 18*B*a^8*b^8 - 4*B*a^9*b^7 - 36*B*a^10*b^6 + 6*B*a^11*b^5 + 34*B*a^12*b^4 - 8*B*a^13*b^3 - 12*B*a^14*b^2 + 4*C*a^7*b^9 - 4*C*a^8*b^8 - 16*C*a^9*b^7 + 4*C*a^10*b^6 + 36*C*a^11*b^5 - 40*C*a^13*b^3 + 4*C*a^14*b^2 + 4*B*a^15*b + 16*C*a^15*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(2*B^3*a*b^11 - 4*B^3*b^12 + 16*C^3*a^11*b + 18*B^3*a^2*b^10 - 13*B^3*a^3*b^9 - 36*B^3*a^4*b^8 + 26*B^3*a^5*b^7 + 34*B^3*a^6*b^6 - 24*B^3*a^7*b^5 - 12*B^3*a^8*b^4 + 4*C^3*a^3*b^9 - 16*C^3*a^5*b^7 + 12*C^3*a^6*b^6 + 36*C^3*a^7*b^5 - 24*C^3*a^8*b^4 - 40*C^3*a^9*b^3 + 48*C^3*a^10*b^2 + 12*B^2*C*a*b^11 - 12*B*C^2*a^2*b^10 + 2*B*C^2*a^3*b^9 + 50*B*C^2*a^4*b^8 - 36*B*C^2*a^5*b^7 - 108*B*C^2*a^6*b^6 + 78*B*C^2*a^7*b^5 + 114*B*C^2*a^8*b^4 - 116*B*C^2*a^9*b^3 - 44*B*C^2*a^10*b^2 - 4*B^2*C*a^2*b^10 - 52*B^2*C*a^3*b^9 + 37*B^2*C*a^4*b^8 + 108*B^2*C*a^5*b^7 - 80*B^2*C*a^6*b^6 - 108*B^2*C*a^7*b^5 + 92*B^2*C*a^8*b^4 + 40*B^2*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^12 + 4*C^2*a^12 - 8*B^2*a*b^11 - 8*C^2*a^11*b - 32*B^2*a^2*b^10 + 32*B^2*a^3*b^9 + 57*B^2*a^4*b^8 - 48*B^2*a^5*b^7 - 52*B^2*a^6*b^6 + 32*B^2*a^7*b^5 + 24*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 4*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 28*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 56*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 56*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 52*C^2*a^10*b^2 - 16*B*C*a*b^11 - 8*B*C*a^11*b + 16*B*C*a^2*b^10 + 60*B*C*a^3*b^9 - 64*B*C*a^4*b^8 - 112*B*C*a^5*b^7 + 96*B*C*a^6*b^6 + 112*B*C*a^7*b^5 - 64*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(2*B*a^7*b^9 - 4*B*a^6*b^10 - 4*C*a^16 + 18*B*a^8*b^8 - 4*B*a^9*b^7 - 36*B*a^10*b^6 + 6*B*a^11*b^5 + 34*B*a^12*b^4 - 8*B*a^13*b^3 - 12*B*a^14*b^2 + 4*C*a^7*b^9 - 4*C*a^8*b^8 - 16*C*a^9*b^7 + 4*C*a^10*b^6 + 36*C*a^11*b^5 - 40*C*a^13*b^3 + 4*C*a^14*b^2 + 4*B*a^15*b + 16*C*a^15*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) - (b*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^12 + 4*C^2*a^12 - 8*B^2*a*b^11 - 8*C^2*a^11*b - 32*B^2*a^2*b^10 + 32*B^2*a^3*b^9 + 57*B^2*a^4*b^8 - 48*B^2*a^5*b^7 - 52*B^2*a^6*b^6 + 32*B^2*a^7*b^5 + 24*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 4*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 28*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 56*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 56*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 52*C^2*a^10*b^2 - 16*B*C*a*b^11 - 8*B*C*a^11*b + 16*B*C*a^2*b^10 + 60*B*C*a^3*b^9 - 64*B*C*a^4*b^8 - 112*B*C*a^5*b^7 + 96*B*C*a^6*b^6 + 112*B*C*a^7*b^5 - 64*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(2*B*a^7*b^9 - 4*B*a^6*b^10 - 4*C*a^16 + 18*B*a^8*b^8 - 4*B*a^9*b^7 - 36*B*a^10*b^6 + 6*B*a^11*b^5 + 34*B*a^12*b^4 - 8*B*a^13*b^3 - 12*B*a^14*b^2 + 4*C*a^7*b^9 - 4*C*a^8*b^8 - 16*C*a^9*b^7 + 4*C*a^10*b^6 + 36*C*a^11*b^5 - 40*C*a^13*b^3 + 4*C*a^14*b^2 + 4*B*a^15*b + 16*C*a^15*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*((a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 8*C*a^5 - 5*B*a^2*b^3 + 4*C*a^3*b^2 + 6*B*a^4*b - 2*C*a*b^4)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
934,1,7573,336,16.749462,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^5,x)","-\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-27\,C\,a^5\,b^2+18\,B\,a^4\,b^3+10\,C\,a^3\,b^4-11\,B\,a^2\,b^5-3\,C\,a\,b^6+3\,B\,b^7\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^7-6\,B\,a^2\,b^5-4\,B\,a^3\,b^4+12\,B\,a^4\,b^3-C\,a^2\,b^5+4\,C\,a^3\,b^4+7\,C\,a^4\,b^3-18\,C\,a^5\,b^2+B\,a\,b^6-2\,C\,a\,b^6\right)}{\left(a+b\right)\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,B\,b^7-6\,B\,a^2\,b^5+4\,B\,a^3\,b^4+12\,B\,a^4\,b^3+C\,a^2\,b^5+4\,C\,a^3\,b^4-7\,C\,a^4\,b^3-18\,C\,a^5\,b^2-B\,a\,b^6-2\,C\,a\,b^6\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,1{}\mathrm{i}\right)}{a^4\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3+44\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5-92\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7+156\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9-164\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}+117\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}-48\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+8\,B^2\,b^{16}-8\,B\,C\,a^{15}\,b+16\,B\,C\,a^{14}\,b^2-120\,B\,C\,a^{13}\,b^3-96\,B\,C\,a^{12}\,b^4+168\,B\,C\,a^{11}\,b^5+240\,B\,C\,a^{10}\,b^6-292\,B\,C\,a^9\,b^7-320\,B\,C\,a^8\,b^8+294\,B\,C\,a^7\,b^9+240\,B\,C\,a^6\,b^{10}-222\,B\,C\,a^5\,b^{11}-96\,B\,C\,a^4\,b^{12}+96\,B\,C\,a^3\,b^{13}+16\,B\,C\,a^2\,b^{14}-16\,B\,C\,a\,b^{15}+4\,C^2\,a^{16}-8\,C^2\,a^{15}\,b+80\,C^2\,a^{14}\,b^2+48\,C^2\,a^{13}\,b^3-64\,C^2\,a^{12}\,b^4-120\,C^2\,a^{11}\,b^5+145\,C^2\,a^{10}\,b^6+160\,C^2\,a^9\,b^7-130\,C^2\,a^8\,b^8-120\,C^2\,a^7\,b^9+105\,C^2\,a^6\,b^{10}+48\,C^2\,a^5\,b^{11}-48\,C^2\,a^4\,b^{12}-8\,C^2\,a^3\,b^{13}+8\,C^2\,a^2\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\left(\frac{8\,\left(4\,C\,a^{22}+4\,B\,a^8\,b^{14}-2\,B\,a^9\,b^{13}-26\,B\,a^{10}\,b^{12}+14\,B\,a^{11}\,b^{11}+70\,B\,a^{12}\,b^{10}-30\,B\,a^{13}\,b^9-110\,B\,a^{14}\,b^8+30\,B\,a^{15}\,b^7+110\,B\,a^{16}\,b^6-20\,B\,a^{17}\,b^5-64\,B\,a^{18}\,b^4+12\,B\,a^{19}\,b^3+16\,B\,a^{20}\,b^2-4\,C\,a^9\,b^{13}+2\,C\,a^{10}\,b^{12}+26\,C\,a^{11}\,b^{11}-20\,C\,a^{12}\,b^{10}-64\,C\,a^{13}\,b^9+44\,C\,a^{14}\,b^8+96\,C\,a^{15}\,b^7-36\,C\,a^{16}\,b^6-104\,C\,a^{17}\,b^5+14\,C\,a^{18}\,b^4+70\,C\,a^{19}\,b^3-8\,C\,a^{20}\,b^2-4\,B\,a^{21}\,b-20\,C\,a^{21}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3+44\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5-92\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7+156\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9-164\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}+117\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}-48\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+8\,B^2\,b^{16}-8\,B\,C\,a^{15}\,b+16\,B\,C\,a^{14}\,b^2-120\,B\,C\,a^{13}\,b^3-96\,B\,C\,a^{12}\,b^4+168\,B\,C\,a^{11}\,b^5+240\,B\,C\,a^{10}\,b^6-292\,B\,C\,a^9\,b^7-320\,B\,C\,a^8\,b^8+294\,B\,C\,a^7\,b^9+240\,B\,C\,a^6\,b^{10}-222\,B\,C\,a^5\,b^{11}-96\,B\,C\,a^4\,b^{12}+96\,B\,C\,a^3\,b^{13}+16\,B\,C\,a^2\,b^{14}-16\,B\,C\,a\,b^{15}+4\,C^2\,a^{16}-8\,C^2\,a^{15}\,b+80\,C^2\,a^{14}\,b^2+48\,C^2\,a^{13}\,b^3-64\,C^2\,a^{12}\,b^4-120\,C^2\,a^{11}\,b^5+145\,C^2\,a^{10}\,b^6+160\,C^2\,a^9\,b^7-130\,C^2\,a^8\,b^8-120\,C^2\,a^7\,b^9+105\,C^2\,a^6\,b^{10}+48\,C^2\,a^5\,b^{11}-48\,C^2\,a^4\,b^{12}-8\,C^2\,a^3\,b^{13}+8\,C^2\,a^2\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\left(\frac{8\,\left(4\,C\,a^{22}+4\,B\,a^8\,b^{14}-2\,B\,a^9\,b^{13}-26\,B\,a^{10}\,b^{12}+14\,B\,a^{11}\,b^{11}+70\,B\,a^{12}\,b^{10}-30\,B\,a^{13}\,b^9-110\,B\,a^{14}\,b^8+30\,B\,a^{15}\,b^7+110\,B\,a^{16}\,b^6-20\,B\,a^{17}\,b^5-64\,B\,a^{18}\,b^4+12\,B\,a^{19}\,b^3+16\,B\,a^{20}\,b^2-4\,C\,a^9\,b^{13}+2\,C\,a^{10}\,b^{12}+26\,C\,a^{11}\,b^{11}-20\,C\,a^{12}\,b^{10}-64\,C\,a^{13}\,b^9+44\,C\,a^{14}\,b^8+96\,C\,a^{15}\,b^7-36\,C\,a^{16}\,b^6-104\,C\,a^{17}\,b^5+14\,C\,a^{18}\,b^4+70\,C\,a^{19}\,b^3-8\,C\,a^{20}\,b^2-4\,B\,a^{21}\,b-20\,C\,a^{21}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}{\frac{16\,\left(16\,B^3\,a^{12}\,b^4+48\,B^3\,a^{11}\,b^5-64\,B^3\,a^{10}\,b^6-64\,B^3\,a^9\,b^7+110\,B^3\,a^8\,b^8+66\,B^3\,a^7\,b^9-110\,B^3\,a^6\,b^{10}-34\,B^3\,a^5\,b^{11}+70\,B^3\,a^4\,b^{12}+11\,B^3\,a^3\,b^{13}-26\,B^3\,a^2\,b^{14}-2\,B^3\,a\,b^{15}+4\,B^3\,b^{16}-52\,B^2\,C\,a^{13}\,b^3-172\,B^2\,C\,a^{12}\,b^4+198\,B^2\,C\,a^{11}\,b^5+170\,B^2\,C\,a^{10}\,b^6-324\,B^2\,C\,a^9\,b^7-184\,B^2\,C\,a^8\,b^8+316\,B^2\,C\,a^7\,b^9+82\,B^2\,C\,a^6\,b^{10}-204\,B^2\,C\,a^5\,b^{11}-27\,B^2\,C\,a^4\,b^{12}+78\,B^2\,C\,a^3\,b^{13}+6\,B^2\,C\,a^2\,b^{14}-12\,B^2\,C\,a\,b^{15}+56\,B\,C^2\,a^{14}\,b^2+204\,B\,C^2\,a^{13}\,b^3-204\,B\,C^2\,a^{12}\,b^4-136\,B\,C^2\,a^{11}\,b^5+318\,B\,C^2\,a^{10}\,b^6+179\,B\,C^2\,a^9\,b^7-302\,B\,C^2\,a^8\,b^8-62\,B\,C^2\,a^7\,b^9+198\,B\,C^2\,a^6\,b^{10}+21\,B\,C^2\,a^5\,b^{11}-78\,B\,C^2\,a^4\,b^{12}-6\,B\,C^2\,a^3\,b^{13}+12\,B\,C^2\,a^2\,b^{14}-20\,C^3\,a^{15}\,b-80\,C^3\,a^{14}\,b^2+70\,C^3\,a^{13}\,b^3+30\,C^3\,a^{12}\,b^4-104\,C^3\,a^{11}\,b^5-61\,C^3\,a^{10}\,b^6+96\,C^3\,a^9\,b^7+14\,C^3\,a^8\,b^8-64\,C^3\,a^7\,b^9-5\,C^3\,a^6\,b^{10}+26\,C^3\,a^5\,b^{11}+2\,C^3\,a^4\,b^{12}-4\,C^3\,a^3\,b^{13}\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3+44\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5-92\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7+156\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9-164\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}+117\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}-48\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+8\,B^2\,b^{16}-8\,B\,C\,a^{15}\,b+16\,B\,C\,a^{14}\,b^2-120\,B\,C\,a^{13}\,b^3-96\,B\,C\,a^{12}\,b^4+168\,B\,C\,a^{11}\,b^5+240\,B\,C\,a^{10}\,b^6-292\,B\,C\,a^9\,b^7-320\,B\,C\,a^8\,b^8+294\,B\,C\,a^7\,b^9+240\,B\,C\,a^6\,b^{10}-222\,B\,C\,a^5\,b^{11}-96\,B\,C\,a^4\,b^{12}+96\,B\,C\,a^3\,b^{13}+16\,B\,C\,a^2\,b^{14}-16\,B\,C\,a\,b^{15}+4\,C^2\,a^{16}-8\,C^2\,a^{15}\,b+80\,C^2\,a^{14}\,b^2+48\,C^2\,a^{13}\,b^3-64\,C^2\,a^{12}\,b^4-120\,C^2\,a^{11}\,b^5+145\,C^2\,a^{10}\,b^6+160\,C^2\,a^9\,b^7-130\,C^2\,a^8\,b^8-120\,C^2\,a^7\,b^9+105\,C^2\,a^6\,b^{10}+48\,C^2\,a^5\,b^{11}-48\,C^2\,a^4\,b^{12}-8\,C^2\,a^3\,b^{13}+8\,C^2\,a^2\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\left(\frac{8\,\left(4\,C\,a^{22}+4\,B\,a^8\,b^{14}-2\,B\,a^9\,b^{13}-26\,B\,a^{10}\,b^{12}+14\,B\,a^{11}\,b^{11}+70\,B\,a^{12}\,b^{10}-30\,B\,a^{13}\,b^9-110\,B\,a^{14}\,b^8+30\,B\,a^{15}\,b^7+110\,B\,a^{16}\,b^6-20\,B\,a^{17}\,b^5-64\,B\,a^{18}\,b^4+12\,B\,a^{19}\,b^3+16\,B\,a^{20}\,b^2-4\,C\,a^9\,b^{13}+2\,C\,a^{10}\,b^{12}+26\,C\,a^{11}\,b^{11}-20\,C\,a^{12}\,b^{10}-64\,C\,a^{13}\,b^9+44\,C\,a^{14}\,b^8+96\,C\,a^{15}\,b^7-36\,C\,a^{16}\,b^6-104\,C\,a^{17}\,b^5+14\,C\,a^{18}\,b^4+70\,C\,a^{19}\,b^3-8\,C\,a^{20}\,b^2-4\,B\,a^{21}\,b-20\,C\,a^{21}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}-\frac{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3+44\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5-92\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7+156\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9-164\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}+117\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}-48\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+8\,B^2\,b^{16}-8\,B\,C\,a^{15}\,b+16\,B\,C\,a^{14}\,b^2-120\,B\,C\,a^{13}\,b^3-96\,B\,C\,a^{12}\,b^4+168\,B\,C\,a^{11}\,b^5+240\,B\,C\,a^{10}\,b^6-292\,B\,C\,a^9\,b^7-320\,B\,C\,a^8\,b^8+294\,B\,C\,a^7\,b^9+240\,B\,C\,a^6\,b^{10}-222\,B\,C\,a^5\,b^{11}-96\,B\,C\,a^4\,b^{12}+96\,B\,C\,a^3\,b^{13}+16\,B\,C\,a^2\,b^{14}-16\,B\,C\,a\,b^{15}+4\,C^2\,a^{16}-8\,C^2\,a^{15}\,b+80\,C^2\,a^{14}\,b^2+48\,C^2\,a^{13}\,b^3-64\,C^2\,a^{12}\,b^4-120\,C^2\,a^{11}\,b^5+145\,C^2\,a^{10}\,b^6+160\,C^2\,a^9\,b^7-130\,C^2\,a^8\,b^8-120\,C^2\,a^7\,b^9+105\,C^2\,a^6\,b^{10}+48\,C^2\,a^5\,b^{11}-48\,C^2\,a^4\,b^{12}-8\,C^2\,a^3\,b^{13}+8\,C^2\,a^2\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\left(\frac{8\,\left(4\,C\,a^{22}+4\,B\,a^8\,b^{14}-2\,B\,a^9\,b^{13}-26\,B\,a^{10}\,b^{12}+14\,B\,a^{11}\,b^{11}+70\,B\,a^{12}\,b^{10}-30\,B\,a^{13}\,b^9-110\,B\,a^{14}\,b^8+30\,B\,a^{15}\,b^7+110\,B\,a^{16}\,b^6-20\,B\,a^{17}\,b^5-64\,B\,a^{18}\,b^4+12\,B\,a^{19}\,b^3+16\,B\,a^{20}\,b^2-4\,C\,a^9\,b^{13}+2\,C\,a^{10}\,b^{12}+26\,C\,a^{11}\,b^{11}-20\,C\,a^{12}\,b^{10}-64\,C\,a^{13}\,b^9+44\,C\,a^{14}\,b^8+96\,C\,a^{15}\,b^7-36\,C\,a^{16}\,b^6-104\,C\,a^{17}\,b^5+14\,C\,a^{18}\,b^4+70\,C\,a^{19}\,b^3-8\,C\,a^{20}\,b^2-4\,B\,a^{21}\,b-20\,C\,a^{21}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(10\,C\,a^7-8\,B\,a^6\,b-5\,C\,a^5\,b^2+8\,B\,a^4\,b^3+7\,C\,a^3\,b^4-7\,B\,a^2\,b^5-2\,C\,a\,b^6+2\,B\,b^7\right)\,1{}\mathrm{i}}{d\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1i)*(B*b - C*a)*1i)/(a^4*d) - ((4*tan(c/2 + (d*x)/2)^3*(3*B*b^7 - 11*B*a^2*b^5 + 18*B*a^4*b^3 + 10*C*a^3*b^4 - 27*C*a^5*b^2 - 3*C*a*b^6))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)) + (tan(c/2 + (d*x)/2)*(2*B*b^7 - 6*B*a^2*b^5 - 4*B*a^3*b^4 + 12*B*a^4*b^3 - C*a^2*b^5 + 4*C*a^3*b^4 + 7*C*a^4*b^3 - 18*C*a^5*b^2 + B*a*b^6 - 2*C*a*b^6))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^5*(2*B*b^7 - 6*B*a^2*b^5 + 4*B*a^3*b^4 + 12*B*a^4*b^3 + C*a^2*b^5 + 4*C*a^3*b^4 - 7*C*a^4*b^3 - 18*C*a^5*b^2 - B*a*b^6 - 2*C*a*b^6))/((a^3*b - a^4)*(a + b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*1i))/(a^4*d) + (b*atan(((b*((a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^16 + 4*C^2*a^16 - 8*B^2*a*b^15 - 8*C^2*a^15*b - 48*B^2*a^2*b^14 + 48*B^2*a^3*b^13 + 117*B^2*a^4*b^12 - 120*B^2*a^5*b^11 - 164*B^2*a^6*b^10 + 160*B^2*a^7*b^9 + 156*B^2*a^8*b^8 - 120*B^2*a^9*b^7 - 92*B^2*a^10*b^6 + 48*B^2*a^11*b^5 + 44*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 4*B^2*a^14*b^2 + 8*C^2*a^2*b^14 - 8*C^2*a^3*b^13 - 48*C^2*a^4*b^12 + 48*C^2*a^5*b^11 + 105*C^2*a^6*b^10 - 120*C^2*a^7*b^9 - 130*C^2*a^8*b^8 + 160*C^2*a^9*b^7 + 145*C^2*a^10*b^6 - 120*C^2*a^11*b^5 - 64*C^2*a^12*b^4 + 48*C^2*a^13*b^3 + 80*C^2*a^14*b^2 - 16*B*C*a*b^15 - 8*B*C*a^15*b + 16*B*C*a^2*b^14 + 96*B*C*a^3*b^13 - 96*B*C*a^4*b^12 - 222*B*C*a^5*b^11 + 240*B*C*a^6*b^10 + 294*B*C*a^7*b^9 - 320*B*C*a^8*b^8 - 292*B*C*a^9*b^7 + 240*B*C*a^10*b^6 + 168*B*C*a^11*b^5 - 96*B*C*a^12*b^4 - 120*B*C*a^13*b^3 + 16*B*C*a^14*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*((8*(4*C*a^22 + 4*B*a^8*b^14 - 2*B*a^9*b^13 - 26*B*a^10*b^12 + 14*B*a^11*b^11 + 70*B*a^12*b^10 - 30*B*a^13*b^9 - 110*B*a^14*b^8 + 30*B*a^15*b^7 + 110*B*a^16*b^6 - 20*B*a^17*b^5 - 64*B*a^18*b^4 + 12*B*a^19*b^3 + 16*B*a^20*b^2 - 4*C*a^9*b^13 + 2*C*a^10*b^12 + 26*C*a^11*b^11 - 20*C*a^12*b^10 - 64*C*a^13*b^9 + 44*C*a^14*b^8 + 96*C*a^15*b^7 - 36*C*a^16*b^6 - 104*C*a^17*b^5 + 14*C*a^18*b^4 + 70*C*a^19*b^3 - 8*C*a^20*b^2 - 4*B*a^21*b - 20*C*a^21*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^16 + 4*C^2*a^16 - 8*B^2*a*b^15 - 8*C^2*a^15*b - 48*B^2*a^2*b^14 + 48*B^2*a^3*b^13 + 117*B^2*a^4*b^12 - 120*B^2*a^5*b^11 - 164*B^2*a^6*b^10 + 160*B^2*a^7*b^9 + 156*B^2*a^8*b^8 - 120*B^2*a^9*b^7 - 92*B^2*a^10*b^6 + 48*B^2*a^11*b^5 + 44*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 4*B^2*a^14*b^2 + 8*C^2*a^2*b^14 - 8*C^2*a^3*b^13 - 48*C^2*a^4*b^12 + 48*C^2*a^5*b^11 + 105*C^2*a^6*b^10 - 120*C^2*a^7*b^9 - 130*C^2*a^8*b^8 + 160*C^2*a^9*b^7 + 145*C^2*a^10*b^6 - 120*C^2*a^11*b^5 - 64*C^2*a^12*b^4 + 48*C^2*a^13*b^3 + 80*C^2*a^14*b^2 - 16*B*C*a*b^15 - 8*B*C*a^15*b + 16*B*C*a^2*b^14 + 96*B*C*a^3*b^13 - 96*B*C*a^4*b^12 - 222*B*C*a^5*b^11 + 240*B*C*a^6*b^10 + 294*B*C*a^7*b^9 - 320*B*C*a^8*b^8 - 292*B*C*a^9*b^7 + 240*B*C*a^10*b^6 + 168*B*C*a^11*b^5 - 96*B*C*a^12*b^4 - 120*B*C*a^13*b^3 + 16*B*C*a^14*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*((8*(4*C*a^22 + 4*B*a^8*b^14 - 2*B*a^9*b^13 - 26*B*a^10*b^12 + 14*B*a^11*b^11 + 70*B*a^12*b^10 - 30*B*a^13*b^9 - 110*B*a^14*b^8 + 30*B*a^15*b^7 + 110*B*a^16*b^6 - 20*B*a^17*b^5 - 64*B*a^18*b^4 + 12*B*a^19*b^3 + 16*B*a^20*b^2 - 4*C*a^9*b^13 + 2*C*a^10*b^12 + 26*C*a^11*b^11 - 20*C*a^12*b^10 - 64*C*a^13*b^9 + 44*C*a^14*b^8 + 96*C*a^15*b^7 - 36*C*a^16*b^6 - 104*C*a^17*b^5 + 14*C*a^18*b^4 + 70*C*a^19*b^3 - 8*C*a^20*b^2 - 4*B*a^21*b - 20*C*a^21*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/((16*(4*B^3*b^16 - 2*B^3*a*b^15 - 20*C^3*a^15*b - 26*B^3*a^2*b^14 + 11*B^3*a^3*b^13 + 70*B^3*a^4*b^12 - 34*B^3*a^5*b^11 - 110*B^3*a^6*b^10 + 66*B^3*a^7*b^9 + 110*B^3*a^8*b^8 - 64*B^3*a^9*b^7 - 64*B^3*a^10*b^6 + 48*B^3*a^11*b^5 + 16*B^3*a^12*b^4 - 4*C^3*a^3*b^13 + 2*C^3*a^4*b^12 + 26*C^3*a^5*b^11 - 5*C^3*a^6*b^10 - 64*C^3*a^7*b^9 + 14*C^3*a^8*b^8 + 96*C^3*a^9*b^7 - 61*C^3*a^10*b^6 - 104*C^3*a^11*b^5 + 30*C^3*a^12*b^4 + 70*C^3*a^13*b^3 - 80*C^3*a^14*b^2 - 12*B^2*C*a*b^15 + 12*B*C^2*a^2*b^14 - 6*B*C^2*a^3*b^13 - 78*B*C^2*a^4*b^12 + 21*B*C^2*a^5*b^11 + 198*B*C^2*a^6*b^10 - 62*B*C^2*a^7*b^9 - 302*B*C^2*a^8*b^8 + 179*B*C^2*a^9*b^7 + 318*B*C^2*a^10*b^6 - 136*B*C^2*a^11*b^5 - 204*B*C^2*a^12*b^4 + 204*B*C^2*a^13*b^3 + 56*B*C^2*a^14*b^2 + 6*B^2*C*a^2*b^14 + 78*B^2*C*a^3*b^13 - 27*B^2*C*a^4*b^12 - 204*B^2*C*a^5*b^11 + 82*B^2*C*a^6*b^10 + 316*B^2*C*a^7*b^9 - 184*B^2*C*a^8*b^8 - 324*B^2*C*a^9*b^7 + 170*B^2*C*a^10*b^6 + 198*B^2*C*a^11*b^5 - 172*B^2*C*a^12*b^4 - 52*B^2*C*a^13*b^3))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^16 + 4*C^2*a^16 - 8*B^2*a*b^15 - 8*C^2*a^15*b - 48*B^2*a^2*b^14 + 48*B^2*a^3*b^13 + 117*B^2*a^4*b^12 - 120*B^2*a^5*b^11 - 164*B^2*a^6*b^10 + 160*B^2*a^7*b^9 + 156*B^2*a^8*b^8 - 120*B^2*a^9*b^7 - 92*B^2*a^10*b^6 + 48*B^2*a^11*b^5 + 44*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 4*B^2*a^14*b^2 + 8*C^2*a^2*b^14 - 8*C^2*a^3*b^13 - 48*C^2*a^4*b^12 + 48*C^2*a^5*b^11 + 105*C^2*a^6*b^10 - 120*C^2*a^7*b^9 - 130*C^2*a^8*b^8 + 160*C^2*a^9*b^7 + 145*C^2*a^10*b^6 - 120*C^2*a^11*b^5 - 64*C^2*a^12*b^4 + 48*C^2*a^13*b^3 + 80*C^2*a^14*b^2 - 16*B*C*a*b^15 - 8*B*C*a^15*b + 16*B*C*a^2*b^14 + 96*B*C*a^3*b^13 - 96*B*C*a^4*b^12 - 222*B*C*a^5*b^11 + 240*B*C*a^6*b^10 + 294*B*C*a^7*b^9 - 320*B*C*a^8*b^8 - 292*B*C*a^9*b^7 + 240*B*C*a^10*b^6 + 168*B*C*a^11*b^5 - 96*B*C*a^12*b^4 - 120*B*C*a^13*b^3 + 16*B*C*a^14*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*((8*(4*C*a^22 + 4*B*a^8*b^14 - 2*B*a^9*b^13 - 26*B*a^10*b^12 + 14*B*a^11*b^11 + 70*B*a^12*b^10 - 30*B*a^13*b^9 - 110*B*a^14*b^8 + 30*B*a^15*b^7 + 110*B*a^16*b^6 - 20*B*a^17*b^5 - 64*B*a^18*b^4 + 12*B*a^19*b^3 + 16*B*a^20*b^2 - 4*C*a^9*b^13 + 2*C*a^10*b^12 + 26*C*a^11*b^11 - 20*C*a^12*b^10 - 64*C*a^13*b^9 + 44*C*a^14*b^8 + 96*C*a^15*b^7 - 36*C*a^16*b^6 - 104*C*a^17*b^5 + 14*C*a^18*b^4 + 70*C*a^19*b^3 - 8*C*a^20*b^2 - 4*B*a^21*b - 20*C*a^21*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) - (b*((a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*B^2*b^16 + 4*C^2*a^16 - 8*B^2*a*b^15 - 8*C^2*a^15*b - 48*B^2*a^2*b^14 + 48*B^2*a^3*b^13 + 117*B^2*a^4*b^12 - 120*B^2*a^5*b^11 - 164*B^2*a^6*b^10 + 160*B^2*a^7*b^9 + 156*B^2*a^8*b^8 - 120*B^2*a^9*b^7 - 92*B^2*a^10*b^6 + 48*B^2*a^11*b^5 + 44*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 4*B^2*a^14*b^2 + 8*C^2*a^2*b^14 - 8*C^2*a^3*b^13 - 48*C^2*a^4*b^12 + 48*C^2*a^5*b^11 + 105*C^2*a^6*b^10 - 120*C^2*a^7*b^9 - 130*C^2*a^8*b^8 + 160*C^2*a^9*b^7 + 145*C^2*a^10*b^6 - 120*C^2*a^11*b^5 - 64*C^2*a^12*b^4 + 48*C^2*a^13*b^3 + 80*C^2*a^14*b^2 - 16*B*C*a*b^15 - 8*B*C*a^15*b + 16*B*C*a^2*b^14 + 96*B*C*a^3*b^13 - 96*B*C*a^4*b^12 - 222*B*C*a^5*b^11 + 240*B*C*a^6*b^10 + 294*B*C*a^7*b^9 - 320*B*C*a^8*b^8 - 292*B*C*a^9*b^7 + 240*B*C*a^10*b^6 + 168*B*C*a^11*b^5 - 96*B*C*a^12*b^4 - 120*B*C*a^13*b^3 + 16*B*C*a^14*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*((8*(4*C*a^22 + 4*B*a^8*b^14 - 2*B*a^9*b^13 - 26*B*a^10*b^12 + 14*B*a^11*b^11 + 70*B*a^12*b^10 - 30*B*a^13*b^9 - 110*B*a^14*b^8 + 30*B*a^15*b^7 + 110*B*a^16*b^6 - 20*B*a^17*b^5 - 64*B*a^18*b^4 + 12*B*a^19*b^3 + 16*B*a^20*b^2 - 4*C*a^9*b^13 + 2*C*a^10*b^12 + 26*C*a^11*b^11 - 20*C*a^12*b^10 - 64*C*a^13*b^9 + 44*C*a^14*b^8 + 96*C*a^15*b^7 - 36*C*a^16*b^6 - 104*C*a^17*b^5 + 14*C*a^18*b^4 + 70*C*a^19*b^3 - 8*C*a^20*b^2 - 4*B*a^21*b - 20*C*a^21*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 10*C*a^7 - 7*B*a^2*b^5 + 8*B*a^4*b^3 + 7*C*a^3*b^4 - 5*C*a^5*b^2 - 8*B*a^6*b - 2*C*a*b^6)*1i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
935,0,-1,517,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
936,0,-1,413,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
937,0,-1,324,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x), x)","F"
938,0,-1,366,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
939,0,-1,362,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
940,0,-1,435,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
941,0,-1,538,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
942,0,-1,628,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
943,0,-1,505,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
944,0,-1,406,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x), x)","F"
945,0,-1,443,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
946,0,-1,426,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
947,0,-1,442,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
948,0,-1,540,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
949,0,-1,650,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^4*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
950,0,-1,610,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
951,0,-1,502,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x), x)","F"
952,0,-1,521,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
953,0,-1,505,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
954,0,-1,507,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
955,0,-1,549,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
956,0,-1,652,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
957,0,-1,774,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^5*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
958,0,-1,429,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)), x)","F"
959,0,-1,342,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)), x)","F"
960,0,-1,267,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)), x)","F"
961,0,-1,317,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/2), x)","F"
962,0,-1,358,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
963,0,-1,439,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
964,0,-1,510,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)), x)","F"
965,0,-1,352,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)), x)","F"
966,0,-1,293,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)), x)","F"
967,0,-1,395,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(3/2), x)","F"
968,0,-1,451,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
969,0,-1,552,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
970,0,-1,549,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)), x)","F"
971,0,-1,449,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)), x)","F"
972,0,-1,416,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)), x)","F"
973,0,-1,541,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(5/2), x)","F"
974,0,-1,618,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
975,0,-1,448,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b), x)","F"
976,0,-1,382,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/2)*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b), x)","F"
977,0,-1,316,0.000000,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(1/2), x)","F"
978,0,-1,212,0.000000,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(3/2), x)","F"
979,0,-1,379,0.000000,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(5/2), x)","F"
980,0,-1,519,0.000000,"\text{Not used}","int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(7/2),x)","\int \frac{\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b)/(a + b/cos(c + d*x))^(7/2), x)","F"
981,0,-1,266,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
982,0,-1,230,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
983,0,-1,192,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
984,0,-1,152,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
985,0,-1,146,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
986,0,-1,156,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
987,0,-1,194,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
988,0,-1,230,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
989,0,-1,266,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\int \frac{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2), x)","F"
990,0,-1,343,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
991,0,-1,289,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
992,0,-1,241,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
993,0,-1,224,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
994,0,-1,225,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
995,0,-1,242,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
996,0,-1,290,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
997,0,-1,397,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
998,0,-1,334,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
999,0,-1,319,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1000,0,-1,313,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
1001,0,-1,317,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
1002,0,-1,336,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
1003,0,-1,401,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2), x)","F"
1004,0,-1,515,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^4*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1005,0,-1,441,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1006,0,-1,419,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1007,0,-1,409,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
1008,0,-1,429,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
1009,0,-1,426,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
1010,0,-1,444,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2), x)","F"
1011,0,-1,516,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(13/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(13/2), x)","F"
1012,0,-1,296,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)), x)","F"
1013,0,-1,218,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)), x)","F"
1014,0,-1,178,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)), x)","F"
1015,0,-1,157,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
1016,0,-1,207,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
1017,0,-1,269,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(5/2)), x)","F"
1018,0,-1,342,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(7/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(7/2)), x)","F"
1019,0,-1,447,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2, x)","F"
1020,0,-1,363,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2, x)","F"
1021,0,-1,299,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2, x)","F"
1022,0,-1,317,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
1023,0,-1,406,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
1024,0,-1,507,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)), x)","F"
1025,0,-1,667,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3, x)","F"
1026,0,-1,556,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3, x)","F"
1027,0,-1,469,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3, x)","F"
1028,0,-1,478,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3, x)","F"
1029,0,-1,486,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
1030,0,-1,598,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
1031,0,-1,447,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1032,0,-1,346,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1033,0,-1,258,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1034,0,-1,277,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1035,0,-1,273,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
1036,0,-1,360,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
1037,0,-1,457,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
1038,0,-1,551,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1039,0,-1,446,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1040,0,-1,353,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1041,0,-1,340,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1042,0,-1,356,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
1043,0,-1,359,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
1044,0,-1,455,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
1045,0,-1,550,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1046,0,-1,453,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1047,0,-1,427,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1048,0,-1,419,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(5/2), x)","F"
1049,0,-1,441,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(7/2), x)","F"
1050,0,-1,452,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(9/2), x)","F"
1051,0,-1,565,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(1/cos(c + d*x))^(11/2), x)","F"
1052,0,-1,350,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1053,0,-1,260,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1054,0,-1,219,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
1055,0,-1,216,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
1056,0,-1,291,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
1057,0,-1,380,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)), x)","F"
1058,0,-1,253,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A\,a+\frac{A\,b+B\,a}{\cos\left(c+d\,x\right)}+\frac{B\,b}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1059,0,-1,393,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
1060,0,-1,311,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
1061,0,-1,249,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
1062,0,-1,350,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
1063,0,-1,461,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
1064,0,-1,563,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
1065,0,-1,447,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
1066,0,-1,378,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
1067,0,-1,401,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
1068,0,-1,521,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
1069,0,-1,663,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)), x)","F"
1070,0,-1,248,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",0,"int((a + b/cos(c + d*x))^(2/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1071,0,-1,248,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/3)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1072,0,-1,245,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(1/3), x)","F"
1073,0,-1,245,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(a + b/cos(c + d*x))^(2/3), x)","F"
1074,0,-1,137,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^m*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^m\,\left(\frac{B\,b^2}{\cos\left(c+d\,x\right)}-C\,a^2+\frac{C\,b^2}{{\cos\left(c+d\,x\right)}^2}+B\,a\,b\right) \,d x","Not used",0,"int((a + b/cos(c + d*x))^m*((B*b^2)/cos(c + d*x) - C*a^2 + (C*b^2)/cos(c + d*x)^2 + B*a*b), x)","F"
1075,1,87,80,4.708096,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2),x)","-\frac{2\,A\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*A*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1076,1,80,80,4.578373,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2),x)","\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,A\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*A*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1077,1,60,50,4.721877,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2),x)","\frac{2\,C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1078,1,53,48,0.202768,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
1079,1,60,44,5.185106,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2),x)","\frac{2\,A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1080,1,60,48,5.062684,"\text{Not used}","int((A + C/cos(c + d*x)^2)/cos(c + d*x)^(1/2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1081,1,87,80,4.926821,"\text{Not used}","int((A + C/cos(c + d*x)^2)/cos(c + d*x)^(3/2),x)","\frac{2\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1082,1,87,80,5.243184,"\text{Not used}","int((A + C/cos(c + d*x)^2)/cos(c + d*x)^(5/2),x)","\frac{2\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))","B"
1083,1,166,165,5.184229,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1084,1,139,134,0.445081,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1085,1,112,101,4.569479,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1086,1,112,95,0.745969,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1087,1,123,95,5.225097,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)),x)","\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1088,1,150,132,6.090496,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1089,1,177,165,6.208072,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))","B"
1090,1,266,230,5.482549,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1091,1,242,197,5.466087,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,C\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1092,1,177,164,5.234450,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (4*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1093,1,188,158,5.342413,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1094,1,161,154,5.362741,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1095,1,202,156,6.236970,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2,x)","\frac{6\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,C\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*C*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*C*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1096,1,229,197,6.312357,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/cos(c + d*x)^(1/2),x)","\frac{30\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,C\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,C\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(30*C*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 84*C*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*C*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1097,1,482,230,6.757212,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\frac{4\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{4\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{3\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{16\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{81\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{64\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{16\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(4*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((7*A*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (4*C*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (3*C*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((9*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (16*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((81*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (64*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*C*a^2*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (16*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
1098,1,360,279,5.647879,"\text{Not used}","int(cos(c + d*x)^(13/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(15/2)*sin(c + d*x)*hypergeom([1/2, 15/4], 19/4, cos(c + d*x)^2))/(15*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
1099,1,332,246,5.419226,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^3*ellipticF(c/2 + (d*x)/2, 2) + C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1100,1,283,213,5.065746,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1101,1,269,215,5.010586,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + A*a^3*ellipticF(c/2 + (d*x)/2, 2) + A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1102,1,237,211,5.621635,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1103,1,279,213,6.039842,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1104,1,279,213,7.835799,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3,x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+\frac{6\,C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,C\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,C\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + ((2*C*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*C*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*C*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*C*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1105,1,308,246,7.268209,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/cos(c + d*x)^(1/2),x)","\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{70\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,C\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,C\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (70*C*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 270*C*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 210*C*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*C*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1106,1,621,279,7.415503,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^3)/cos(c + d*x)^(3/2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{11\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{42\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{7\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{231\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{10\,C\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{51\,A\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{40\,C\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{15\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{15\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{275\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{33\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{168\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{119\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{11/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{231\,d}","Not used",1,"(8*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2)*((11*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (42*C*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (7*C*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))))/(231*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((9*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (10*C*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*C*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((51*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*A*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (40*C*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (15*C*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*C*a^3*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2))))/(15*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((275*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (33*A*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (168*C*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (119*C*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*C*a^3*sin(c + d*x))/(cos(c + d*x)^(11/2)*(1 - cos(c + d*x)^2)^(1/2))))/(231*d)","B"
1107,0,-1,192,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1108,0,-1,159,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1109,0,-1,122,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1110,0,-1,84,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1111,0,-1,112,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))), x)","F"
1112,0,-1,150,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))), x)","F"
1113,0,-1,192,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))), x)","F"
1114,0,-1,196,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1115,0,-1,161,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1116,0,-1,130,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1117,0,-1,125,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^2), x)","F"
1118,0,-1,151,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^2), x)","F"
1119,0,-1,189,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^2), x)","F"
1120,0,-1,250,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
1121,0,-1,209,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
1122,0,-1,186,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
1123,0,-1,184,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^3), x)","F"
1124,0,-1,180,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3), x)","F"
1125,0,-1,209,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3), x)","F"
1126,0,-1,242,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3), x)","F"
1127,0,-1,213,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
1128,0,-1,168,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
1129,0,-1,122,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
1130,0,-1,136,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
1131,0,-1,135,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2), x)","F"
1132,0,-1,144,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
1133,0,-1,189,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
1134,0,-1,234,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2), x)","F"
1135,0,-1,266,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(11/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
1136,0,-1,219,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
1137,0,-1,169,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
1138,0,-1,183,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
1139,0,-1,189,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
1140,0,-1,191,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2), x)","F"
1141,0,-1,191,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
1142,0,-1,238,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
1143,0,-1,285,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
1144,0,-1,313,0.000000,"\text{Not used}","int(cos(c + d*x)^(13/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{13/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(13/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1145,0,-1,266,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(11/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1146,0,-1,216,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1147,0,-1,230,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1148,0,-1,230,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1149,0,-1,244,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1150,0,-1,238,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2), x)","F"
1151,0,-1,238,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
1152,0,-1,285,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
1153,0,-1,332,0.000000,"\text{Not used}","int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C/cos(c + d*x)^2)*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
1154,0,-1,244,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1155,0,-1,201,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1156,0,-1,156,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1157,0,-1,175,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1158,0,-1,173,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
1159,0,-1,223,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
1160,0,-1,266,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
1161,0,-1,268,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
1162,0,-1,221,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
1163,0,-1,172,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
1164,0,-1,185,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
1165,0,-1,228,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
1166,0,-1,285,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
1167,0,-1,315,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
1168,0,-1,266,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
1169,0,-1,219,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
1170,0,-1,174,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
1171,0,-1,232,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
1172,0,-1,277,0.000000,"\text{Not used}","int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
1173,1,87,111,4.440695,"\text{Not used}","int(cos(c + d*x)^(9/2)*(B/cos(c + d*x) + C/cos(c + d*x)^2),x)","-\frac{2\,B\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*B*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1174,1,80,87,4.234790,"\text{Not used}","int(cos(c + d*x)^(7/2)*(B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,B\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*B*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1175,1,53,61,0.169780,"\text{Not used}","int(cos(c + d*x)^(5/2)*(B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
1176,1,33,35,0.222021,"\text{Not used}","int(cos(c + d*x)^(3/2)*(B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}","Not used",1,"(2*B*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*ellipticF(c/2 + (d*x)/2, 2))/d","B"
1177,1,60,57,4.392694,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1178,1,87,83,4.702042,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/cos(c + d*x)^(1/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1179,1,87,111,4.789676,"\text{Not used}","int((B/cos(c + d*x) + C/cos(c + d*x)^2)/cos(c + d*x)^(3/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1180,1,123,123,4.228239,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,A\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*A*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1181,1,96,93,4.598468,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,A\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*A*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1182,1,69,65,4.113695,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*B*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
1183,1,76,61,0.282639,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1184,1,103,87,0.383975,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/cos(c + d*x)^(1/2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1185,1,108,123,4.522931,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/cos(c + d*x)^(3/2),x)","\frac{6\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 10*B*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*A*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
1186,1,108,147,5.511843,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/cos(c + d*x)^(5/2),x)","\frac{30\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+42\,B\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(30*C*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 42*B*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*A*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
1187,1,254,175,5.213484,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1188,1,216,142,0.544914,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1189,1,162,106,4.366775,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1190,1,146,98,5.109655,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1191,1,184,103,5.555205,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1192,1,217,141,5.906468,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{6\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1193,1,223,177,6.441416,"\text{Not used}","int(((a + a/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{6\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{30\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+42\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (30*C*a*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*A*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 42*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
1194,1,404,251,5.972318,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1195,1,369,215,5.299779,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,C\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1196,1,280,179,5.099385,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d - (4*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1197,1,237,170,5.319603,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1198,1,245,170,5.905371,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1199,1,313,174,7.203356,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{6\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,C\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*C*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*C*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1200,1,346,215,7.463607,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{6\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,B\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,B\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{30\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,C\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,C\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*B*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*B*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*B*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (30*C*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 84*C*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*C*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1201,1,688,251,7.581279,"\text{Not used}","int(((a + a/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{8\,\left(\frac{B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{18\,B\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{16\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{81\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{72\,B\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{18\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{64\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{14\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{11\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{21\,d}","Not used",1,"(8*((B*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)))*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((9*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (18*B*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (16*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((81*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (72*B*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (18*B*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (64*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*C*a^2*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((14*A*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (11*B*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (3*B*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (8*C*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*C*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))))/(21*d)","B"
1202,1,507,267,5.708624,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^3*ellipticF(c/2 + (d*x)/2, 2) + C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1203,1,430,231,5.493616,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + B*a^3*ellipticF(c/2 + (d*x)/2, 2) + B*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1204,1,376,227,5.464288,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + A*a^3*ellipticF(c/2 + (d*x)/2, 2) + A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*B*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1205,1,358,226,6.015707,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1206,1,408,231,7.187870,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*B*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1207,1,436,231,8.156793,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{2\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+\frac{6\,C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,C\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,C\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + ((2*C*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*C*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*C*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*C*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1208,1,457,267,8.266460,"\text{Not used}","int(((a + a/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+\frac{6\,B\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,B\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,B\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{70\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,C\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,C\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + ((2*B*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*B*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*B*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*B*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (70*C*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 270*C*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 210*C*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*C*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1209,1,764,310,6.263661,"\text{Not used}","int(cos(c + d*x)^(13/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(3\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,C\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}-\frac{8\,\left(\frac{13\,A\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{117\,d}-\frac{136\,\left(\frac{11\,A\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{51\,A\,a^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{23}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21945\,d}-\frac{2\,\left(\frac{66\,C\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{17\,C\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{77\,d}-\frac{2\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{165\,A\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{578\,A\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{127\,A\,a^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{1155\,d}+\frac{B\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{160\,A\,a^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{21}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{663\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{208\,C\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{385\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(3*C*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*C*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*C*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) - (8*((13*A*a^4*cos(c + d*x)^(9/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (5*A*a^4*cos(c + d*x)^(13/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(117*d) - (136*((11*A*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (51*A*a^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 15/4], 23/4, cos(c + d*x)^2))/(21945*d) - (2*((66*C*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (17*C*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(77*d) - (2*hypergeom([1/2, 15/4], 19/4, cos(c + d*x)^2)*((165*A*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (578*A*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (127*A*a^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(1155*d) + (B*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (160*A*a^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 21/4, cos(c + d*x)^2))/(663*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (208*C*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 19/4, cos(c + d*x)^2))/(385*d*(sin(c + d*x)^2)^(1/2))","B"
1210,1,601,274,5.997583,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(3\,B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,B\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}+\frac{2\,\left(4\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{2\,\left(\frac{66\,B\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{17\,B\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{77\,d}+\frac{A\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{8\,A\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{208\,B\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{385\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(3*B*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*B*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*B*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) + (2*(4*C*a^4*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a^4*ellipticF(c/2 + (d*x)/2, 2) + 2*C*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (2*((66*B*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (17*B*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(77*d) + (A*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (8*A*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (208*B*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 19/4, cos(c + d*x)^2))/(385*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1211,1,548,270,5.973289,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(3\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,A\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}+\frac{2\,\left(4\,B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,B\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{2\,\left(\frac{66\,A\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{17\,A\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{77\,d}+\frac{4\,C\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{8\,A\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{208\,A\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{385\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(3*A*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*A*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*A*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) + (2*(4*B*a^4*ellipticE(c/2 + (d*x)/2, 2) + 3*B*a^4*ellipticF(c/2 + (d*x)/2, 2) + 2*B*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (2*((66*A*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (17*A*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(77*d) + (4*C*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*C*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*C*a^4*ellipticF(c/2 + (d*x)/2, 2))/d - (8*A*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (208*A*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 19/4, cos(c + d*x)^2))/(385*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1212,1,468,269,6.098187,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(4\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,\left(12\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+19\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}+\frac{4\,B\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{8\,A\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(4*A*a^4*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a^4*ellipticF(c/2 + (d*x)/2, 2) + 2*A*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*(12*C*a^4*ellipticE(c/2 + (d*x)/2, 2) + 19*C*a^4*ellipticF(c/2 + (d*x)/2, 2) + C*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) + (4*B*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*B*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*B*a^4*ellipticF(c/2 + (d*x)/2, 2))/d - (8*A*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) + (2*B*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*B*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (8*C*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1213,1,525,267,8.026711,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(12\,B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+19\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}+\frac{2\,\left(C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{2\,\left(\frac{34\,C\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d}+\frac{4\,A\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(12*B*a^4*ellipticE(c/2 + (d*x)/2, 2) + 19*B*a^4*ellipticF(c/2 + (d*x)/2, 2) + B*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) + (2*(C*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*C*a^4*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*((34*C*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (C*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(5*d) + (4*A*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*A*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*A*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*A*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (8*B*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (8*C*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1214,1,560,271,9.529539,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(12\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+19\,A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}+\frac{2\,\left(B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{2\,\left(\frac{34\,B\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d}+\frac{2\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(12*A*a^4*ellipticE(c/2 + (d*x)/2, 2) + 19*A*a^4*ellipticF(c/2 + (d*x)/2, 2) + A*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) + (2*(B*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*B*a^4*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*((34*B*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (B*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(5*d) + (2*C*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (8*A*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (8*B*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))","B"
1215,1,724,274,10.768503,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{2\,\left(\frac{34\,A\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d}+\frac{8\,\left(\frac{11\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{3\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d}-\frac{8\,\left(\frac{61\,C\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{289\,C\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{66\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{32\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*A*a^4*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*((34*A*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (A*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(5*d) + (8*((11*C*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (3*C*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(21*d) - (8*((61*C*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (5*C*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((289*C*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (66*C*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*C*a^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (2*B*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (8*A*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (8*A*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (32*C*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1216,1,830,310,10.129078,"\text{Not used}","int(((a + a/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{8\,\left(\frac{11\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{3\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d}-\frac{8\,\left(\frac{61\,B\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{135\,d}+\frac{8\,\left(\frac{13\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{45\,d}+\frac{8\,\left(\frac{75\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{7\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{231\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{289\,B\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{66\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{377\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{218\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{21\,C\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{11/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{231\,d}+\frac{2\,A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{32\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{32\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(8*((11*B*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (3*B*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(21*d) - (8*((61*B*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (5*B*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2))/(135*d) + (8*((13*C*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*C*a^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(45*d) + (8*((75*C*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (7*C*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(231*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((289*B*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (66*B*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*B*a^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((377*C*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (218*C*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (21*C*a^4*sin(c + d*x))/(cos(c + d*x)^(11/2)*(sin(c + d*x)^2)^(1/2))))/(231*d) + (2*A*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (8*A*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (32*B*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (32*C*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
1217,0,-1,210,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1218,0,-1,174,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1219,0,-1,134,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1220,0,-1,93,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x)), x)","F"
1221,0,-1,122,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))), x)","F"
1222,0,-1,165,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))), x)","F"
1223,0,-1,210,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))), x)","F"
1224,0,-1,258,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1225,0,-1,214,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1226,0,-1,180,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1227,0,-1,144,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^2, x)","F"
1228,0,-1,133,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^2), x)","F"
1229,0,-1,167,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^2), x)","F"
1230,0,-1,211,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^2), x)","F"
1231,0,-1,250,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^2), x)","F"
1232,0,-1,273,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
1233,0,-1,234,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
1234,0,-1,201,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^3, x)","F"
1235,0,-1,193,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^3), x)","F"
1236,0,-1,191,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3), x)","F"
1237,0,-1,229,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3), x)","F"
1238,0,-1,268,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3), x)","F"
1239,0,-1,278,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4, x)","F"
1240,0,-1,244,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^4, x)","F"
1241,0,-1,232,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^4),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^4), x)","F"
1242,0,-1,229,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^4),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^4), x)","F"
1243,0,-1,234,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^4),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^4), x)","F"
1244,0,-1,276,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^4),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^4), x)","F"
1245,0,-1,226,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1246,0,-1,178,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1247,0,-1,129,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1248,0,-1,140,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1249,0,-1,139,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1250,0,-1,151,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1251,0,-1,199,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1252,0,-1,247,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
1253,0,-1,284,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1254,0,-1,232,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1255,0,-1,181,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1256,0,-1,192,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1257,0,-1,197,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1258,0,-1,203,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1259,0,-1,201,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1260,0,-1,253,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1261,0,-1,303,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
1262,0,-1,334,0.000000,"\text{Not used}","int(cos(c + d*x)^(13/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{13/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(13/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1263,0,-1,284,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1264,0,-1,231,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1265,0,-1,242,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1266,0,-1,243,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1267,0,-1,253,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1268,0,-1,253,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1269,0,-1,253,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1270,0,-1,301,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1271,0,-1,353,0.000000,"\text{Not used}","int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + a/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
1272,0,-1,257,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1273,0,-1,211,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1274,0,-1,163,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1275,0,-1,178,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1276,0,-1,181,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
1277,0,-1,235,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
1278,0,-1,281,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
1279,0,-1,184,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A\,a+\frac{A\,b+B\,a}{\cos\left(c+d\,x\right)}+\frac{B\,b}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(1/2), x)","F"
1280,0,-1,283,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
1281,0,-1,233,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
1282,0,-1,181,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(3/2), x)","F"
1283,0,-1,189,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
1284,0,-1,242,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
1285,0,-1,300,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
1286,0,-1,333,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
1287,0,-1,281,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
1288,0,-1,231,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + a/cos(c + d*x))^(5/2), x)","F"
1289,0,-1,183,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
1290,0,-1,241,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
1291,0,-1,294,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
1292,1,254,190,5.369240,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,C\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1293,1,216,154,5.075399,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*b*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*A*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1294,1,162,116,5.017707,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*b*ellipticF(c/2 + (d*x)/2, 2))/d - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1295,1,146,106,5.412615,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1296,1,184,112,6.343108,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1297,1,217,152,7.092553,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{6\,C\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*b*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1298,1,223,190,7.802520,"\text{Not used}","int(((a + b/cos(c + d*x))*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{6\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{30\,C\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+42\,B\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (30*C*b*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*A*b*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 42*B*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
1299,1,366,250,5.883914,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,B\,b^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*A*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1300,1,303,202,5.686974,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{C\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*C*a*b*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1301,1,260,186,5.928641,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{B\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(B*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*B*a*b*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticF(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*C*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1302,1,268,180,6.501289,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{A\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a*b*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1303,1,310,201,7.541968,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{6\,C\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,C\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*C*b^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*C*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*C*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1304,1,343,249,8.045584,"\text{Not used}","int(((a + b/cos(c + d*x))^2*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{6\,B\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,B\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,B\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{30\,C\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,C\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,C\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*B*b^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*B*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*B*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (30*C*b^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*C*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 84*C*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1305,1,514,361,6.202808,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(C\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{B\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a^2\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^3*ellipticE(c/2 + (d*x)/2, 2) + C*a*b^2*ellipticF(c/2 + (d*x)/2, 2) + C*a*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (B*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*A*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a^2*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1306,1,452,296,6.096436,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,C\,a^2\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*b^3*ellipticE(c/2 + (d*x)/2, 2) + B*a*b^2*ellipticF(c/2 + (d*x)/2, 2) + B*a*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (3*C*a^2*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1307,1,398,277,6.088745,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,B\,a^2\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*b^3*ellipticE(c/2 + (d*x)/2, 2) + A*a*b^2*ellipticF(c/2 + (d*x)/2, 2) + A*a*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (3*B*a^2*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*C*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (6*A*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1308,1,379,267,7.236867,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^3+3\,C\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^2\right)}{d}+\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,A\,a^2\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a^2*b*ellipticF(c/2 + (d*x)/2, 2)))/d + (B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*B*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (6*B*a*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (3*A*a^2*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*B*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1309,1,414,274,8.675137,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^3+3\,B\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^2\right)}{d}+\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*B*a^2*b*ellipticF(c/2 + (d*x)/2, 2)))/d + (A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1310,1,442,294,10.660431,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^3+3\,A\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^2\right)}{d}+\frac{\frac{2\,C\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,C\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,C\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,A\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a^2*b*ellipticF(c/2 + (d*x)/2, 2)))/d + ((2*C*b^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*C*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*C*a^2*b*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*C*a*b^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*A*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1311,1,463,357,10.700154,"\text{Not used}","int(((a + b/cos(c + d*x))^3*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{\frac{2\,B\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,B\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,B\,a^2\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,B\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{70\,C\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,C\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,C\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"((2*B*b^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*B*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*B*a^2*b*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*B*a*b^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (70*C*b^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 210*C*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*C*a^2*b*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 270*C*a*b^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*A*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1312,1,600,404,6.807320,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(C\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,C\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,b^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a^3\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^3\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,B\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^4*ellipticF(c/2 + (d*x)/2, 2) + 4*C*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + 2*C*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*C*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*b^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*a^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a^3*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^3*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a^3*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a^2*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (12*B*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1313,1,547,377,6.494527,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,B\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,B\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,B\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,A\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,C\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,C\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a^3\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^3\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,A\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*b^4*ellipticF(c/2 + (d*x)/2, 2) + 4*B*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + 2*B*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*B*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*A*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*C*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*C*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*C*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*C*b^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (8*A*a^3*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^3*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (12*A*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1314,1,516,371,6.889254,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,A\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,\left(C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,C\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,C\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{8\,B\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,B\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a^3\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*b^4*ellipticF(c/2 + (d*x)/2, 2) + 4*A*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + 2*A*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*A*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*(C*a^4*ellipticF(c/2 + (d*x)/2, 2) + 12*C*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + C*a^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*C*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (8*B*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (4*B*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*B*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*B*b^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (8*A*a^3*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (8*C*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1315,1,524,388,9.997585,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,B\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,B\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,A\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^4*ellipticF(c/2 + (d*x)/2, 2) + 12*B*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + B*a^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*B*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*A*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (8*C*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*A*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (2*A*b^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (12*C*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1316,1,559,384,12.768054,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{2\,\left(A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,A\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,A\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,B\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^4*ellipticF(c/2 + (d*x)/2, 2) + 12*A*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + A*a^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*A*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (8*B*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a*b^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (12*B*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1317,1,866,401,14.867888,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^4*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{4\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{7\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{3\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,C\,b^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,C\,b^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{45\,C\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{28\,C\,b^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,C\,b^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,C\,b^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{216\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{32\,C\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(8*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((4*C*a*b^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (7*C*a^3*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (3*C*a*b^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((7*C*b^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (5*C*b^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (54*C*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((45*C*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (28*C*b^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (12*C*b^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*C*b^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2)) + (216*C*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (54*C*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (2*A*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (8*A*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a*b^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (32*C*a*b^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (12*A*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1318,0,-1,209,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)), x)","F"
1319,0,-1,147,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)), x)","F"
1320,0,-1,97,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x)), x)","F"
1321,0,-1,118,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))), x)","F"
1322,0,-1,158,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))), x)","F"
1323,0,-1,236,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))), x)","F"
1324,0,-1,346,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2, x)","F"
1325,0,-1,257,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^2, x)","F"
1326,0,-1,239,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^2), x)","F"
1327,0,-1,307,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^2), x)","F"
1328,0,-1,387,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^2), x)","F"
1329,0,-1,538,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3, x)","F"
1330,0,-1,426,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^3, x)","F"
1331,0,-1,423,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^3), x)","F"
1332,0,-1,409,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^3), x)","F"
1333,0,-1,496,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^3), x)","F"
1334,0,-1,457,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1335,0,-1,360,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1336,0,-1,273,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1337,0,-1,277,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1338,0,-1,258,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1339,0,-1,346,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1340,0,-1,447,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1341,0,-1,455,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1342,0,-1,359,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1343,0,-1,356,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1344,0,-1,340,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1345,0,-1,353,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1346,0,-1,446,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1347,0,-1,551,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1348,0,-1,565,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(11/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1349,0,-1,452,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1350,0,-1,441,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1351,0,-1,419,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1352,0,-1,427,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1353,0,-1,453,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2), x)","F"
1354,0,-1,550,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1355,0,-1,674,0.000000,"\text{Not used}","int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b/cos(c + d*x))^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1356,0,-1,380,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1357,0,-1,291,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1358,0,-1,216,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1359,0,-1,219,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1360,0,-1,260,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(1/2)), x)","F"
1361,0,-1,350,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(1/2)), x)","F"
1362,0,-1,208,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A\,a+\frac{A\,b+B\,a}{\cos\left(c+d\,x\right)}+\frac{B\,b}{{\cos\left(c+d\,x\right)}^2}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A*a + (A*b + B*a)/cos(c + d*x) + (B*b)/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(1/2), x)","F"
1363,0,-1,461,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
1364,0,-1,350,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
1365,0,-1,249,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(3/2), x)","F"
1366,0,-1,311,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(3/2)), x)","F"
1367,0,-1,393,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(3/2)), x)","F"
1368,0,-1,663,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
1369,0,-1,521,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
1370,0,-1,401,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x) + C/cos(c + d*x)^2))/(a + b/cos(c + d*x))^(5/2), x)","F"
1371,0,-1,378,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"
1372,0,-1,447,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"
1373,0,-1,563,0.000000,"\text{Not used}","int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}+\frac{C}{{\cos\left(c+d\,x\right)}^2}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x) + C/cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"