1,0,-1,171,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(5/2), x)","F"
2,0,-1,136,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(3/2), x)","F"
3,0,-1,104,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(1/2), x)","F"
4,0,-1,82,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\sqrt{\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(1/2), x)","F"
5,0,-1,116,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(3/2), x)","F"
6,0,-1,147,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(5/2), x)","F"
7,0,-1,119,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3))/cos(c + d*x)^2, x)","F"
8,0,-1,116,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3))/cos(c + d*x),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3))/cos(c + d*x), x)","F"
9,0,-1,112,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(b/cos(c + d*x))^(2/3), x)","F"
10,0,-1,115,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int(cos(c + d*x)*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3), x)","F"
11,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3), x)","F"
12,0,-1,119,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3))/cos(c + d*x)^2, x)","F"
13,0,-1,116,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3))/cos(c + d*x),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3))/cos(c + d*x), x)","F"
14,0,-1,112,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(b/cos(c + d*x))^(4/3), x)","F"
15,0,-1,115,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int(cos(c + d*x)*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3), x)","F"
16,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3), x)","F"
17,0,-1,117,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)), x)","F"
18,0,-1,114,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)), x)","F"
19,0,-1,114,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{B}{\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))/(b/cos(c + d*x))^(2/3), x)","F"
20,0,-1,114,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(b/cos(c + d*x))^(2/3)), x)","F"
21,0,-1,117,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^2*(b/cos(c + d*x))^(2/3)), x)","F"
22,0,-1,117,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)), x)","F"
23,0,-1,114,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)), x)","F"
24,0,-1,114,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(b/cos(c + d*x))^(4/3),x)","\int \frac{A+\frac{B}{\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))/(b/cos(c + d*x))^(4/3), x)","F"
25,0,-1,114,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(b/cos(c + d*x))^(4/3)), x)","F"
26,0,-1,117,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^2*(b/cos(c + d*x))^(4/3)), x)","F"
27,0,-1,167,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3)*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^(4/3)*(1/cos(c + d*x))^m, x)","F"
28,0,-1,165,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^m, x)","F"
29,0,-1,165,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^m, x)","F"
30,0,-1,165,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(1/3),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(1/3), x)","F"
31,0,-1,165,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(2/3),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(2/3), x)","F"
32,0,-1,173,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(4/3),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^m)/(b/cos(c + d*x))^(4/3), x)","F"
33,0,-1,172,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^n*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n*(1/cos(c + d*x))^m, x)","F"
34,0,-1,143,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^n)/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n)/cos(c + d*x)^2, x)","F"
35,0,-1,136,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^n)/cos(c + d*x),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n)/cos(c + d*x), x)","F"
36,0,-1,137,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^n,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int((A + B/cos(c + d*x))*(b/cos(c + d*x))^n, x)","F"
37,0,-1,151,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(b/cos(c + d*x))^n,x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cos(c + d*x)*(A + B/cos(c + d*x))*(b/cos(c + d*x))^n, x)","F"
38,0,-1,153,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(b/cos(c + d*x))^n,x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(b/cos(c + d*x))^n, x)","F"
39,0,-1,163,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(3/2), x)","F"
40,0,-1,163,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n*(1/cos(c + d*x))^(1/2), x)","F"
41,0,-1,163,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(1/2), x)","F"
42,0,-1,163,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(b/cos(c + d*x))^n)/(1/cos(c + d*x))^(3/2), x)","F"
43,1,198,134,4.750812,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/cos(c + d*x)^4,x)","\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+B\right)}{4\,d}-\frac{\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{29\,A\,a}{6}-\frac{13\,B\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,a}{3}+\frac{116\,B\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{35\,A\,a}{6}-\frac{19\,B\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+\frac{13\,B\,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,"(3*a*atanh(tan(c/2 + (d*x)/2))*(A + B))/(4*d) - (tan(c/2 + (d*x)/2)*((13*A*a)/4 + (13*B*a)/4) + tan(c/2 + (d*x)/2)^9*((3*A*a)/4 + (3*B*a)/4) - tan(c/2 + (d*x)/2)^7*((29*A*a)/6 + (13*B*a)/6) - tan(c/2 + (d*x)/2)^3*((35*A*a)/6 + (19*B*a)/6) + tan(c/2 + (d*x)/2)^5*((20*A*a)/3 + (116*B*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"
44,1,166,106,4.617318,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{\left(-A\,a-\frac{3\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{7\,A\,a}{3}+\frac{49\,B\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{13\,A\,a}{3}-\frac{31\,B\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,B\,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\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + (13*B*a)/4) - tan(c/2 + (d*x)/2)^7*(A*a + (3*B*a)/4) - tan(c/2 + (d*x)/2)^3*((13*A*a)/3 + (31*B*a)/12) + tan(c/2 + (d*x)/2)^5*((7*A*a)/3 + (49*B*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*B))/(4*d)","B"
45,1,126,86,3.987638,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+B\right)}{d}-\frac{\left(A\,a+B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a-\frac{4\,B\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+3\,B\,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))*(A + B))/d - (tan(c/2 + (d*x)/2)*(3*A*a + 3*B*a) + tan(c/2 + (d*x)/2)^5*(A*a + B*a) - tan(c/2 + (d*x)/2)^3*(4*A*a + (4*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))","B"
46,1,94,56,2.731662,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/cos(c + d*x),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a+3\,B\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a+B\,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\,A+B\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a + 3*B*a) - tan(c/2 + (d*x)/2)^3*(2*A*a + B*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*A + B))/d","B"
47,1,100,32,2.234497,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x)),x)","\frac{B\,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\,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{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}","Not used",1,"(B*a*tan(c + d*x))/d + (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 + (2*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
48,1,100,32,2.148537,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(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\,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}","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*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","B"
49,1,50,47,2.086903,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x)),x)","\frac{A\,a\,x}{2}+B\,a\,x+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*a*x)/2 + B*a*x + (A*a*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (A*a*sin(2*c + 2*d*x))/(4*d)","B"
50,1,84,77,2.101969,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x)),x)","\frac{A\,a\,x}{2}+\frac{B\,a\,x}{2}+\frac{3\,A\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,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 + (3*A*a*sin(c + d*x))/(4*d) + (B*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"
51,1,184,97,4.668126,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x)),x)","\frac{\left(\frac{3\,A\,a}{4}+B\,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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{31\,A\,a}{12}+\frac{13\,B\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,B\,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\right)}{4\,\left(\frac{3\,A\,a}{4}+B\,a\right)}\right)\,\left(3\,A+4\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*B*a) + tan(c/2 + (d*x)/2)^7*((3*A*a)/4 + B*a) + tan(c/2 + (d*x)/2)^3*((31*A*a)/12 + (13*B*a)/3) + tan(c/2 + (d*x)/2)^5*((49*A*a)/12 + (7*B*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*A + 4*B))/(4*((3*A*a)/4 + B*a)))*(3*A + 4*B))/(4*d)","B"
52,1,212,125,4.807986,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + a/cos(c + d*x)),x)","\frac{\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{13\,A\,a}{6}+\frac{29\,B\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,B\,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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+\frac{13\,B\,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{3\,a\,\mathrm{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{4\,\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}\right)}\right)\,\left(A+B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + (13*B*a)/4) + tan(c/2 + (d*x)/2)^9*((3*A*a)/4 + (3*B*a)/4) + tan(c/2 + (d*x)/2)^7*((13*A*a)/6 + (29*B*a)/6) + tan(c/2 + (d*x)/2)^3*((19*A*a)/6 + (35*B*a)/6) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*B*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)) + (3*a*atan((3*a*tan(c/2 + (d*x)/2)*(A + B))/(4*((3*A*a)/4 + (3*B*a)/4)))*(A + B))/(4*d)","B"
53,1,224,169,4.606489,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,A+6\,B\right)}{4\,d}-\frac{\left(\frac{7\,A\,a^2}{4}+\frac{3\,B\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{49\,A\,a^2}{6}-7\,B\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{40\,A\,a^2}{3}+\frac{72\,B\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{79\,A\,a^2}{6}-9\,B\,a^2\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}\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*A + 6*B))/(4*d) - (tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + (13*B*a^2)/2) + tan(c/2 + (d*x)/2)^9*((7*A*a^2)/4 + (3*B*a^2)/2) - tan(c/2 + (d*x)/2)^7*((49*A*a^2)/6 + 7*B*a^2) - tan(c/2 + (d*x)/2)^3*((79*A*a^2)/6 + 9*B*a^2) + tan(c/2 + (d*x)/2)^5*((40*A*a^2)/3 + (72*B*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"
54,1,183,138,4.465115,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{\left(-2\,A\,a^2-\frac{7\,B\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{22\,A\,a^2}{3}+\frac{77\,B\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{34\,A\,a^2}{3}-\frac{83\,B\,a^2}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A\,a^2+\frac{25\,B\,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(A+\frac{7\,B}{8}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(6*A*a^2 + (25*B*a^2)/4) - tan(c/2 + (d*x)/2)^7*(2*A*a^2 + (7*B*a^2)/4) + tan(c/2 + (d*x)/2)^5*((22*A*a^2)/3 + (77*B*a^2)/12) - tan(c/2 + (d*x)/2)^3*((34*A*a^2)/3 + (83*B*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))*(A + (7*B)/8))/d","B"
55,1,145,103,3.809167,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2)/cos(c + d*x),x)","\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,A}{2}+B\right)}{d}-\frac{\left(3\,A\,a^2+2\,B\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,A\,a^2-\frac{16\,B\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(5\,A\,a^2+6\,B\,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*A)/2 + B))/d - (tan(c/2 + (d*x)/2)*(5*A*a^2 + 6*B*a^2) + tan(c/2 + (d*x)/2)^5*(3*A*a^2 + 2*B*a^2) - tan(c/2 + (d*x)/2)^3*(8*A*a^2 + (16*B*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"
56,1,162,82,2.005196,"\text{Not used}","int((A + B/cos(c + d*x))*(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{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)}{d}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","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 + (3*B*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)) + (2*B*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^2*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
57,1,161,73,2.006359,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(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{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{B\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","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 + (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 + (B*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
58,1,141,88,2.048638,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{B\,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{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{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(2*A*a^2*sin(c + d*x))/d + (B*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 + (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 + (A*a^2*sin(2*c + 2*d*x))/(4*d)","B"
59,1,98,102,1.889893,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2,x)","A\,a^2\,x+\frac{3\,B\,a^2\,x}{2}+\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{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,"A*a^2*x + (3*B*a^2*x)/2 + (7*A*a^2*sin(c + d*x))/(4*d) + (2*B*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))/(12*d) + (B*a^2*sin(2*c + 2*d*x))/(4*d)","B"
60,1,134,135,1.932583,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2,x)","\frac{7\,A\,a^2\,x}{8}+B\,a^2\,x+\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{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}","Not used",1,"(7*A*a^2*x)/8 + B*a^2*x + (3*A*a^2*sin(c + d*x))/(2*d) + (7*B*a^2*sin(c + d*x))/(4*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)","B"
61,1,247,160,4.680103,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2,x)","\frac{\left(\frac{3\,A\,a^2}{2}+\frac{7\,B\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(7\,A\,a^2+\frac{49\,B\,a^2}{6}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(9\,A\,a^2+\frac{79\,B\,a^2}{6}\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}\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\right)}{4\,\left(\frac{3\,A\,a^2}{2}+\frac{7\,B\,a^2}{4}\right)}\right)\,\left(6\,A+7\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a^2)/2 + (25*B*a^2)/4) + tan(c/2 + (d*x)/2)^9*((3*A*a^2)/2 + (7*B*a^2)/4) + tan(c/2 + (d*x)/2)^7*(7*A*a^2 + (49*B*a^2)/6) + tan(c/2 + (d*x)/2)^3*(9*A*a^2 + (79*B*a^2)/6) + tan(c/2 + (d*x)/2)^5*((72*A*a^2)/5 + (40*B*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*A + 7*B))/(4*((3*A*a^2)/2 + (7*B*a^2)/4)))*(6*A + 7*B))/(4*d)","B"
62,1,262,210,4.626479,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{\left(-\frac{13\,A\,a^3}{4}-\frac{23\,B\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{221\,A\,a^3}{12}+\frac{391\,B\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{429\,A\,a^3}{10}-\frac{759\,B\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{499\,A\,a^3}{10}+\frac{969\,B\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{419\,A\,a^3}{12}-\frac{211\,B\,a^3}{8}\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}\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(26\,A+23\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (105*B*a^3)/8) - tan(c/2 + (d*x)/2)^11*((13*A*a^3)/4 + (23*B*a^3)/8) - tan(c/2 + (d*x)/2)^3*((419*A*a^3)/12 + (211*B*a^3)/8) + tan(c/2 + (d*x)/2)^9*((221*A*a^3)/12 + (391*B*a^3)/24) - tan(c/2 + (d*x)/2)^7*((429*A*a^3)/10 + (759*B*a^3)/20) + tan(c/2 + (d*x)/2)^5*((499*A*a^3)/10 + (969*B*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))*(26*A + 23*B))/(8*d)","B"
63,1,224,163,4.595957,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,A+13\,B\right)}{4\,d}-\frac{\left(\frac{15\,A\,a^3}{4}+\frac{13\,B\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{35\,A\,a^3}{2}-\frac{91\,B\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(32\,A\,a^3+\frac{416\,B\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{61\,A\,a^3}{2}-\frac{133\,B\,a^3}{6}\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}\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*A + 13*B))/(4*d) - (tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + (51*B*a^3)/4) + tan(c/2 + (d*x)/2)^9*((15*A*a^3)/4 + (13*B*a^3)/4) - tan(c/2 + (d*x)/2)^7*((35*A*a^3)/2 + (91*B*a^3)/6) - tan(c/2 + (d*x)/2)^3*((61*A*a^3)/2 + (133*B*a^3)/6) + tan(c/2 + (d*x)/2)^5*(32*A*a^3 + (416*B*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"
64,1,185,125,4.473853,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/cos(c + d*x),x)","\frac{\left(-5\,A\,a^3-\frac{15\,B\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{55\,A\,a^3}{3}+\frac{55\,B\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{73\,A\,a^3}{3}-\frac{73\,B\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A\,a^3+\frac{49\,B\,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\,A+3\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(11*A*a^3 + (49*B*a^3)/4) - tan(c/2 + (d*x)/2)^7*(5*A*a^3 + (15*B*a^3)/4) + tan(c/2 + (d*x)/2)^5*((55*A*a^3)/3 + (55*B*a^3)/4) - tan(c/2 + (d*x)/2)^3*((73*A*a^3)/3 + (73*B*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*A + 3*B))/(4*d)","B"
65,1,209,111,2.077950,"\text{Not used}","int((A + B/cos(c + d*x))*(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{5\,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{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{11\,B\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","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 + (5*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/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) + (11*B*a^3*sin(c + d*x))/(3*d*cos(c + d*x)) + (3*B*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (B*a^3*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
66,1,207,108,2.123035,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(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{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{A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\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}","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 + (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 + (A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (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)","B"
67,1,197,117,2.076070,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3,x)","\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{B\,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{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{B\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\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 + (B*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 + (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 + (B*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
68,1,178,125,2.152303,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3,x)","\frac{15\,A\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,B\,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{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{3\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(15*A*a^3*sin(c + d*x))/(4*d) + (3*B*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 + (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 + (3*A*a^3*sin(2*c + 2*d*x))/(4*d) + (A*a^3*sin(3*c + 3*d*x))/(12*d) + (B*a^3*sin(2*c + 2*d*x))/(4*d)","B"
69,1,134,124,2.005253,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3,x)","\frac{15\,A\,a^3\,x}{8}+\frac{5\,B\,a^3\,x}{2}+\frac{13\,A\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{15\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,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{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}","Not used",1,"(15*A*a^3*x)/8 + (5*B*a^3*x)/2 + (13*A*a^3*sin(c + d*x))/(4*d) + (15*B*a^3*sin(c + d*x))/(4*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) + (3*B*a^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(3*c + 3*d*x))/(12*d)","B"
70,1,247,176,4.710065,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{13\,A\,a^3}{4}+\frac{15\,B\,a^3}{4}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,A\,a^3}{15}+32\,B\,a^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}\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}\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\right)}{4\,\left(\frac{13\,A\,a^3}{4}+\frac{15\,B\,a^3}{4}\right)}\right)\,\left(13\,A+15\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (49*B*a^3)/4) + tan(c/2 + (d*x)/2)^9*((13*A*a^3)/4 + (15*B*a^3)/4) + tan(c/2 + (d*x)/2)^7*((91*A*a^3)/6 + (35*B*a^3)/2) + tan(c/2 + (d*x)/2)^3*((133*A*a^3)/6 + (61*B*a^3)/2) + tan(c/2 + (d*x)/2)^5*((416*A*a^3)/15 + 32*B*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))/(4*((13*A*a^3)/4 + (15*B*a^3)/4)))*(13*A + 15*B))/(4*d)","B"
71,1,285,201,4.681085,"\text{Not used}","int(cos(c + d*x)^6*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3,x)","\frac{\left(\frac{23\,A\,a^3}{8}+\frac{13\,B\,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}\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}\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}\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}\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}\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\right)}{8\,\left(\frac{23\,A\,a^3}{8}+\frac{13\,B\,a^3}{4}\right)}\right)\,\left(23\,A+26\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((105*A*a^3)/8 + (51*B*a^3)/4) + tan(c/2 + (d*x)/2)^11*((23*A*a^3)/8 + (13*B*a^3)/4) + tan(c/2 + (d*x)/2)^3*((211*A*a^3)/8 + (419*B*a^3)/12) + tan(c/2 + (d*x)/2)^9*((391*A*a^3)/24 + (221*B*a^3)/12) + tan(c/2 + (d*x)/2)^7*((759*A*a^3)/20 + (429*B*a^3)/10) + tan(c/2 + (d*x)/2)^5*((969*A*a^3)/20 + (499*B*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*A + 26*B))/(8*((23*A*a^3)/8 + (13*B*a^3)/4)))*(23*A + 26*B))/(8*d)","B"
72,1,262,194,4.606357,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4)/cos(c + d*x)^2,x)","\frac{\left(-7\,A\,a^4-\frac{49\,B\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{119\,A\,a^4}{3}+\frac{833\,B\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{462\,A\,a^4}{5}-\frac{1617\,B\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{562\,A\,a^4}{5}+\frac{1967\,B\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{233\,A\,a^4}{3}-\frac{1471\,B\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{207\,B\,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(8\,A+7\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(25*A*a^4 + (207*B*a^4)/8) - tan(c/2 + (d*x)/2)^11*(7*A*a^4 + (49*B*a^4)/8) + tan(c/2 + (d*x)/2)^9*((119*A*a^4)/3 + (833*B*a^4)/24) - tan(c/2 + (d*x)/2)^3*((233*A*a^4)/3 + (1471*B*a^4)/24) - tan(c/2 + (d*x)/2)^7*((462*A*a^4)/5 + (1617*B*a^4)/20) + tan(c/2 + (d*x)/2)^5*((562*A*a^4)/5 + (1967*B*a^4)/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)) + (7*a^4*atanh(tan(c/2 + (d*x)/2))*(8*A + 7*B))/(8*d)","B"
73,1,224,159,4.541995,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4)/cos(c + d*x),x)","\frac{7\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,A+4\,B\right)}{4\,d}-\frac{\left(\frac{35\,A\,a^4}{4}+7\,B\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{245\,A\,a^4}{6}-\frac{98\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{224\,A\,a^4}{3}+\frac{896\,B\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{395\,A\,a^4}{6}-\frac{158\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{93\,A\,a^4}{4}+25\,B\,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,"(7*a^4*atanh(tan(c/2 + (d*x)/2))*(5*A + 4*B))/(4*d) - (tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + 25*B*a^4) + tan(c/2 + (d*x)/2)^9*((35*A*a^4)/4 + 7*B*a^4) - tan(c/2 + (d*x)/2)^7*((245*A*a^4)/6 + (98*B*a^4)/3) - tan(c/2 + (d*x)/2)^3*((395*A*a^4)/6 + (158*B*a^4)/3) + tan(c/2 + (d*x)/2)^5*((224*A*a^4)/3 + (896*B*a^4)/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"
74,1,255,151,2.096768,"\text{Not used}","int((A + B/cos(c + d*x))*(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{35\,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)}{4\,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{20\,B\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{27\,B\,a^4\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{4\,B\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}","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 + (35*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*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) + (20*B*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (27*B*a^4*sin(c + d*x))/(8*d*cos(c + d*x)^2) + (4*B*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (B*a^4*sin(c + d*x))/(4*d*cos(c + d*x)^4)","B"
75,1,254,151,2.099980,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(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{2\,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)}{d}+\frac{12\,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)}{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\,B\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","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 + (2*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/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*B*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (2*B*a^4*sin(c + d*x))/(d*cos(c + d*x)^2) + (B*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
76,1,243,160,2.172031,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4,x)","\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{B\,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{8\,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)}{d}+\frac{13\,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)}{d}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{4\,B\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\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 + (B*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 + (8*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*B*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)) + (4*B*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (A*a^4*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
77,1,242,165,2.229735,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4,x)","\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d}+\frac{4\,B\,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{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)}{d}+\frac{8\,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)}{d}+\frac{A\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}+\frac{B\,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*B*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 + (13*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*B*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) + (B*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (2*A*a^4*cos(c + d*x)*sin(c + d*x))/d + (B*a^4*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
78,1,188,173,2.449883,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4,x)","\frac{105\,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)+144\,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)+24\,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)+21\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+4\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{3\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+12\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)+B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+84\,A\,a^4\,\sin\left(c+d\,x\right)+81\,B\,a^4\,\sin\left(c+d\,x\right)}{12\,d}","Not used",1,"(105*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 144*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 24*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 21*A*a^4*sin(2*c + 2*d*x) + 4*A*a^4*sin(3*c + 3*d*x) + (3*A*a^4*sin(4*c + 4*d*x))/8 + 12*B*a^4*sin(2*c + 2*d*x) + B*a^4*sin(3*c + 3*d*x) + 84*A*a^4*sin(c + d*x) + 81*B*a^4*sin(c + d*x))/(12*d)","B"
79,1,248,158,4.699405,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4,x)","\frac{\left(7\,A\,a^4+\frac{35\,B\,a^4}{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}\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}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{93\,B\,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)}^{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{7\,a^4\,\mathrm{atan}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+5\,B\right)}{4\,\left(7\,A\,a^4+\frac{35\,B\,a^4}{4}\right)}\right)\,\left(4\,A+5\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(25*A*a^4 + (93*B*a^4)/4) + tan(c/2 + (d*x)/2)^9*(7*A*a^4 + (35*B*a^4)/4) + tan(c/2 + (d*x)/2)^7*((98*A*a^4)/3 + (245*B*a^4)/6) + tan(c/2 + (d*x)/2)^3*((158*A*a^4)/3 + (395*B*a^4)/6) + tan(c/2 + (d*x)/2)^5*((896*A*a^4)/15 + (224*B*a^4)/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)) + (7*a^4*atan((7*a^4*tan(c/2 + (d*x)/2)*(4*A + 5*B))/(4*(7*A*a^4 + (35*B*a^4)/4)))*(4*A + 5*B))/(4*d)","B"
80,1,286,220,4.623769,"\text{Not used}","int(cos(c + d*x)^6*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4,x)","\frac{\left(\frac{49\,A\,a^4}{8}+7\,B\,a^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}\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}\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}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+25\,B\,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)}^{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\right)}{8\,\left(\frac{49\,A\,a^4}{8}+7\,B\,a^4\right)}\right)\,\left(7\,A+8\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + 25*B*a^4) + tan(c/2 + (d*x)/2)^11*((49*A*a^4)/8 + 7*B*a^4) + tan(c/2 + (d*x)/2)^9*((833*A*a^4)/24 + (119*B*a^4)/3) + tan(c/2 + (d*x)/2)^3*((1471*A*a^4)/24 + (233*B*a^4)/3) + tan(c/2 + (d*x)/2)^7*((1617*A*a^4)/20 + (462*B*a^4)/5) + tan(c/2 + (d*x)/2)^5*((1967*A*a^4)/20 + (562*B*a^4)/5))/(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))/(8*((49*A*a^4)/8 + 7*B*a^4)))*(7*A + 8*B))/(8*d)","B"
81,1,323,241,4.127897,"\text{Not used}","int(cos(c + d*x)^7*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^4,x)","\frac{\left(\frac{11\,A\,a^4}{2}+\frac{49\,B\,a^4}{8}\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}\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}\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}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(70\,A\,a^4+\frac{523\,B\,a^4}{6}\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}\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\right)}{8\,\left(\frac{11\,A\,a^4}{2}+\frac{49\,B\,a^4}{8}\right)}\right)\,\left(44\,A+49\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((53*A*a^4)/2 + (207*B*a^4)/8) + tan(c/2 + (d*x)/2)^13*((11*A*a^4)/2 + (49*B*a^4)/8) + tan(c/2 + (d*x)/2)^11*((110*A*a^4)/3 + (245*B*a^4)/6) + tan(c/2 + (d*x)/2)^3*(70*A*a^4 + (523*B*a^4)/6) + tan(c/2 + (d*x)/2)^7*((5632*A*a^4)/35 + (896*B*a^4)/5) + tan(c/2 + (d*x)/2)^9*((3113*A*a^4)/30 + (13867*B*a^4)/120) + tan(c/2 + (d*x)/2)^5*((1501*A*a^4)/10 + (19157*B*a^4)/120))/(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))/(8*((11*A*a^4)/2 + (49*B*a^4)/8)))*(44*A + 49*B))/(8*d)","B"
82,1,152,131,2.437025,"\text{Not used}","int((A + B/cos(c + d*x))/(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(A-B\right)}{a\,d}-\frac{\left(3\,A-5\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,B}{3}-4\,A\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A-3\,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)}^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\right)}{a\,d}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2))*(A - B))/(a*d) - (tan(c/2 + (d*x)/2)^5*(3*A - 5*B) - tan(c/2 + (d*x)/2)^3*(4*A - (16*B)/3) + tan(c/2 + (d*x)/2)*(A - 3*B))/(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))/(a*d)","B"
83,1,119,108,2.114438,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^3*(a + a/cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\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}\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-3\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A-B\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)*(A - B))/(a*d) - (2*atanh(tan(c/2 + (d*x)/2))*(A - (3*B)/2))/(a*d) - (tan(c/2 + (d*x)/2)^3*(2*A - 3*B) - tan(c/2 + (d*x)/2)*(2*A - B))/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4))","B"
84,1,79,62,2.033167,"\text{Not used}","int((A + B/cos(c + d*x))/(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-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(A-B\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\right)}{a\,d}","Not used",1,"(2*B*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) + (2*atanh(tan(c/2 + (d*x)/2))*(A - B))/(a*d) - (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
85,1,41,43,1.930695,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + a/cos(c + d*x))),x)","\frac{2\,B\,\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-B\right)}{a\,d}","Not used",1,"(2*B*atanh(tan(c/2 + (d*x)/2)))/(a*d) + (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
86,1,32,35,1.899731,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x)),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\right)}{a}-\frac{A\,d\,x}{a}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)*(A - B))/a - (A*d*x)/a)/d","B"
87,1,65,60,2.001804,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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{x\,\left(A-B\right)}{a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\right)}{a\,d}","Not used",1,"(2*A*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - (x*(A - B))/a + (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
88,1,107,98,2.213265,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x)),x)","\frac{x\,\left(3\,A-2\,B\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\right)}{a\,d}","Not used",1,"(x*(3*A - 2*B))/(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))/(a*d)","B"
89,1,138,122,3.023703,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x)),x)","\frac{\left(5\,A-3\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,A}{3}-4\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-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)}^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(A-B\right)}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(5*A - 3*B) + tan(c/2 + (d*x)/2)^3*((16*A)/3 - 4*B) + tan(c/2 + (d*x)/2)*(3*A - B))/(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*(A - B))/(2*a) + (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
90,1,202,179,1.980345,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^5*(a + a/cos(c + d*x))^2),x)","\frac{\left(5\,A-10\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{40\,B}{3}-8\,A\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-6\,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)}^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{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(A-B\right)}{a^2}+\frac{3\,A-5\,B}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,A-10\,B\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(5*A - 10*B) - tan(c/2 + (d*x)/2)^3*(8*A - (40*B)/3) + tan(c/2 + (d*x)/2)*(3*A - 6*B))/(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)) - (tan(c/2 + (d*x)/2)*((2*(A - B))/a^2 + (3*A - 5*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) + (atanh(tan(c/2 + (d*x)/2))*(7*A - 10*B))/(a^2*d)","B"
91,1,166,156,1.929154,"\text{Not used}","int((A + B/cos(c + d*x))/(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{3\,\left(A-B\right)}{2\,a^2}+\frac{2\,A-4\,B}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-5\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A-3\,B\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\right)}{6\,a^2\,d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A-7\,B\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A - B))/(2*a^2) + (2*A - 4*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(2*A - 5*B) - tan(c/2 + (d*x)/2)*(2*A - 3*B))/(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 - B))/(6*a^2*d) - (atanh(tan(c/2 + (d*x)/2))*(4*A - 7*B))/(a^2*d)","B"
92,1,120,108,1.928544,"\text{Not used}","int((A + B/cos(c + d*x))/(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\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B}{a^2}+\frac{A-3\,B}{2\,a^2}\right)}{d}-\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)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A - 2*B))/(a^2*d) - (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) - (tan(c/2 + (d*x)/2)*((A - B)/a^2 + (A - 3*B)/(2*a^2)))/d - (2*B*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2))","B"
93,1,74,79,1.917555,"\text{Not used}","int((A + B/cos(c + d*x))/(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}{2\,a^2}-\frac{B}{a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}+\frac{2\,B\,\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)*((A - B)/(2*a^2) - B/a^2))/d + (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) + (2*B*atanh(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
94,1,45,65,1.891580,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{2\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A + B))/(2*a^2*d) - (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d)","B"
95,1,65,70,1.926162,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^2,x)","\frac{3\,B\,\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-B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,A\,d\,x}{6\,a^2\,d}","Not used",1,"(3*B*tan(c/2 + (d*x)/2) - 9*A*tan(c/2 + (d*x)/2) + A*tan(c/2 + (d*x)/2)^3 - B*tan(c/2 + (d*x)/2)^3 + 6*A*d*x)/(6*a^2*d)","B"
96,1,109,98,2.040244,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B}{a^2}+\frac{3\,A-B}{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\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A - B)/a^2 + (3*A - B)/(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))/(6*a^2*d)","B"
97,1,154,143,2.065208,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^2,x)","\frac{x\,\left(7\,A-4\,B\right)}{2\,a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B\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\right)}{6\,a^2\,d}","Not used",1,"(x*(7*A - 4*B))/(2*a^2) - (tan(c/2 + (d*x)/2)*((3*(A - B))/(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))/(6*a^2*d)","B"
98,1,187,170,2.081803,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^2,x)","\frac{\left(10\,A-5\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{40\,A}{3}-8\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A-3\,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)}^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\right)}{2\,a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(A-B\right)}{a^2}+\frac{5\,A-3\,B}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(10*A - 5*B) + tan(c/2 + (d*x)/2)^3*((40*A)/3 - 8*B) + tan(c/2 + (d*x)/2)*(6*A - 3*B))/(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))/(2*a^2) + (tan(c/2 + (d*x)/2)*((2*(A - B))/a^2 + (5*A - 3*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d)","B"
99,1,216,202,2.025716,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^5*(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\right)}{2\,a^3}+\frac{3\,\left(3\,A-5\,B\right)}{4\,a^3}+\frac{2\,A-10\,B}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-7\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A-5\,B\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{A-B}{4\,a^3}+\frac{3\,A-5\,B}{12\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(6\,A-13\,B\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A - B))/(2*a^3) + (3*(3*A - 5*B))/(4*a^3) + (2*A - 10*B)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^3*(2*A - 7*B) - tan(c/2 + (d*x)/2)*(2*A - 5*B))/(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 - B)/(4*a^3) + (3*A - 5*B)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d) - (atanh(tan(c/2 + (d*x)/2))*(6*A - 13*B))/(a^3*d)","B"
100,1,168,156,2.038470,"\text{Not used}","int((A + B/cos(c + d*x))/(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\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B\right)}{4\,a^3}-\frac{3\,B}{2\,a^3}+\frac{2\,A-4\,B}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{6\,a^3}+\frac{2\,A-4\,B}{12\,a^3}\right)}{d}-\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)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A - 3*B))/(a^3*d) - (tan(c/2 + (d*x)/2)*((3*(A - B))/(4*a^3) - (3*B)/(2*a^3) + (2*A - 4*B)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d) - (tan(c/2 + (d*x)/2)^3*((A - B)/(6*a^3) + (2*A - 4*B)/(12*a^3)))/d - (2*B*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3))","B"
101,1,124,125,1.976845,"\text{Not used}","int((A + B/cos(c + d*x))/(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}{12\,a^3}+\frac{A-3\,B}{12\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B}{4\,a^3}+\frac{A-3\,B}{4\,a^3}-\frac{A+3\,B}{4\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}+\frac{2\,B\,\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*((A - B)/(12*a^3) + (A - 3*B)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((A - B)/(4*a^3) + (A - 3*B)/(4*a^3) - (A + 3*B)/(4*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d) + (2*B*atanh(tan(c/2 + (d*x)/2)))/(a^3*d)","B"
102,1,66,102,1.918382,"\text{Not used}","int((A + B/cos(c + d*x))/(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\,A+15\,B-3\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+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\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(15*A + 15*B - 3*A*tan(c/2 + (d*x)/2)^4 + 10*B*tan(c/2 + (d*x)/2)^2 + 3*B*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
103,1,66,102,1.922836,"\text{Not used}","int((A + B/cos(c + d*x))/(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\,A+15\,B-10\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,B\,{\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*A + 15*B - 10*A*tan(c/2 + (d*x)/2)^2 + 3*A*tan(c/2 + (d*x)/2)^4 - 3*B*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
104,1,133,108,2.127486,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^3,x)","\frac{A\,x}{a^3}+\frac{{\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)-{\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{B\,\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{B\,{\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)^2*((A*sin(c/2 + (d*x)/2)^3)/3 - (B*sin(c/2 + (d*x)/2)^3)/6) - cos(c/2 + (d*x)/2)^4*((7*A*sin(c/2 + (d*x)/2))/4 - (B*sin(c/2 + (d*x)/2))/4) - (A*sin(c/2 + (d*x)/2)^5)/20 + (B*sin(c/2 + (d*x)/2)^5)/20)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
105,1,155,136,1.982233,"\text{Not used}","int((cos(c + d*x)*(A + B/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(\frac{3\,A}{2\,a^3}+\frac{3\,\left(A-B\right)}{4\,a^3}+\frac{4\,A-2\,B}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{6\,a^3}+\frac{4\,A-2\,B}{12\,a^3}\right)}{d}-\frac{x\,\left(3\,A-B\right)}{a^3}+\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\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*A)/(2*a^3) + (3*(A - B))/(4*a^3) + (4*A - 2*B)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((A - B)/(6*a^3) + (4*A - 2*B)/(12*a^3)))/d - (x*(3*A - B))/a^3 + (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))/(20*a^3*d)","B"
106,1,204,187,1.996611,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^3,x)","\frac{x\,\left(13\,A-6\,B\right)}{2\,a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B\right)}{2\,a^3}+\frac{3\,\left(5\,A-3\,B\right)}{4\,a^3}+\frac{10\,A-2\,B}{4\,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{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{4\,a^3}+\frac{5\,A-3\,B}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}","Not used",1,"(x*(13*A - 6*B))/(2*a^3) - (tan(c/2 + (d*x)/2)*((3*(A - B))/(2*a^3) + (3*(5*A - 3*B))/(4*a^3) + (10*A - 2*B)/(4*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)) + (tan(c/2 + (d*x)/2)^3*((A - B)/(4*a^3) + (5*A - 3*B)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d)","B"
107,1,237,218,2.050201,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^3,x)","\frac{\left(17\,A-7\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{76\,A}{3}-12\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A-5\,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)}^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{5\,\left(A-B\right)}{2\,a^3}+\frac{6\,A-4\,B}{a^3}+\frac{15\,A-5\,B}{4\,a^3}\right)}{d}-\frac{x\,\left(23\,A-13\,B\right)}{2\,a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{3\,a^3}+\frac{6\,A-4\,B}{12\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(17*A - 7*B) + tan(c/2 + (d*x)/2)^3*((76*A)/3 - 12*B) + tan(c/2 + (d*x)/2)*(11*A - 5*B))/(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)*((5*(A - B))/(2*a^3) + (6*A - 4*B)/a^3 + (15*A - 5*B)/(4*a^3)))/d - (x*(23*A - 13*B))/(2*a^3) - (tan(c/2 + (d*x)/2)^3*((A - B)/(3*a^3) + (6*A - 4*B)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d)","B"
108,1,272,238,2.054511,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^6*(a + a/cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{4\,a^4}+\frac{4\,A-6\,B}{8\,a^4}+\frac{5\,A-15\,B}{24\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A-B\right)}{4\,a^4}-\frac{5\,B}{2\,a^4}+\frac{3\,\left(4\,A-6\,B\right)}{4\,a^4}+\frac{3\,\left(5\,A-15\,B\right)}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-9\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A-7\,B\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{3\,\left(A-B\right)}{40\,a^4}+\frac{4\,A-6\,B}{40\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4\,d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(8\,A-21\,B\right)}{a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A - B)/(4*a^4) + (4*A - 6*B)/(8*a^4) + (5*A - 15*B)/(24*a^4)))/d + (tan(c/2 + (d*x)/2)*((5*(A - B))/(4*a^4) - (5*B)/(2*a^4) + (3*(4*A - 6*B))/(4*a^4) + (3*(5*A - 15*B))/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*(2*A - 9*B) - tan(c/2 + (d*x)/2)*(2*A - 7*B))/(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*((3*(A - B))/(40*a^4) + (4*A - 6*B)/(40*a^4)))/d + (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4*d) - (atanh(tan(c/2 + (d*x)/2))*(8*A - 21*B))/(a^4*d)","B"
109,1,237,194,2.030584,"\text{Not used}","int((A + B/cos(c + d*x))/(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-4\,B\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A-B}{20\,a^4}+\frac{3\,A-5\,B}{40\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B}{2\,a^4}+\frac{3\,\left(3\,A-5\,B\right)}{8\,a^4}+\frac{2\,A-10\,B}{4\,a^4}-\frac{2\,A+10\,B}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{8\,a^4}+\frac{3\,A-5\,B}{12\,a^4}+\frac{2\,A-10\,B}{24\,a^4}\right)}{d}-\frac{2\,B\,\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)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*(A - 4*B))/(a^4*d) - (tan(c/2 + (d*x)/2)^5*((A - B)/(20*a^4) + (3*A - 5*B)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)*((A - B)/(2*a^4) + (3*(3*A - 5*B))/(8*a^4) + (2*A - 10*B)/(4*a^4) - (2*A + 10*B)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4*d) - (tan(c/2 + (d*x)/2)^3*((A - B)/(8*a^4) + (3*A - 5*B)/(12*a^4) + (2*A - 10*B)/(24*a^4)))/d - (2*B*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4))","B"
110,1,198,163,2.128011,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^4*(a + a/cos(c + d*x))^4),x)","\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}-\frac{11\,B\,{\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{3\,A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}\right)+{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}-\frac{15\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}\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}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}+\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)}{a^4\,d}","Not used",1,"(cos(c/2 + (d*x)/2)^4*((A*sin(c/2 + (d*x)/2)^3)/8 - (11*B*sin(c/2 + (d*x)/2)^3)/24) + cos(c/2 + (d*x)/2)^2*((3*A*sin(c/2 + (d*x)/2)^5)/40 - (B*sin(c/2 + (d*x)/2)^5)/8) + cos(c/2 + (d*x)/2)^6*((A*sin(c/2 + (d*x)/2))/8 - (15*B*sin(c/2 + (d*x)/2))/8) + (A*sin(c/2 + (d*x)/2)^7)/56 - (B*sin(c/2 + (d*x)/2)^7)/56)/(a^4*d*cos(c/2 + (d*x)/2)^7) + (2*B*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^4*d)","B"
111,1,85,146,2.033436,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^3*(a + a/cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+3\,B\right)}{24\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-3\,B\right)}{40\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{8\,a^4}}{d}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(A + 3*B))/(24*a^4) - (tan(c/2 + (d*x)/2)^5*(A - 3*B))/(40*a^4) - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4) + (tan(c/2 + (d*x)/2)*(A + B))/(8*a^4))/d","B"
112,1,84,138,1.984282,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}^5\,\left(A+B\right)}{40\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{24\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{8\,a^4}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)^5*(A + B))/(40*a^4) + (tan(c/2 + (d*x)/2)^3*(A - B))/(24*a^4) - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4) - (tan(c/2 + (d*x)/2)*(A + B))/(8*a^4))/d","B"
113,1,88,138,1.988463,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}^3\,\left(3\,A+B\right)}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{8\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A-B\right)}{40\,a^4}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)^3*(3*A + B))/(24*a^4) + (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4) - (tan(c/2 + (d*x)/2)*(A + B))/(8*a^4) - (tan(c/2 + (d*x)/2)^5*(3*A - B))/(40*a^4))/d","B"
114,1,163,138,2.034439,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^4,x)","\frac{A\,x}{a^4}-\frac{\left(\frac{52\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}-\frac{12\,B\,\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{23\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}-\frac{16\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}\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{9\,B\,\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{B\,\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 - ((B*sin(c/2 + (d*x)/2))/56 - (A*sin(c/2 + (d*x)/2))/56 + cos(c/2 + (d*x)/2)^2*((5*A*sin(c/2 + (d*x)/2))/28 - (9*B*sin(c/2 + (d*x)/2))/70) + cos(c/2 + (d*x)/2)^6*((52*A*sin(c/2 + (d*x)/2))/21 - (12*B*sin(c/2 + (d*x)/2))/35) - cos(c/2 + (d*x)/2)^4*((16*A*sin(c/2 + (d*x)/2))/21 - (23*B*sin(c/2 + (d*x)/2))/70))/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
115,1,202,166,2.055998,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^4,x)","\frac{\left(\frac{764\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-\frac{52\,B\,\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\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}-\frac{143\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}\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{5\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{28}\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{B\,\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\,d\,x-B\,d\,x}{a^4\,d}+\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}","Not used",1,"((B*sin(c/2 + (d*x)/2))/56 - (A*sin(c/2 + (d*x)/2))/56 + cos(c/2 + (d*x)/2)^2*((8*A*sin(c/2 + (d*x)/2))/35 - (5*B*sin(c/2 + (d*x)/2))/28) - cos(c/2 + (d*x)/2)^4*((143*A*sin(c/2 + (d*x)/2))/105 - (16*B*sin(c/2 + (d*x)/2))/21) + cos(c/2 + (d*x)/2)^6*((764*A*sin(c/2 + (d*x)/2))/105 - (52*B*sin(c/2 + (d*x)/2))/21))/(a^4*d*cos(c/2 + (d*x)/2)^7) - (4*A*d*x - B*d*x)/(a^4*d) + (2*A*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^4*d)","B"
116,1,179,223,1.998366,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^4,x)","\frac{\frac{21\,A\,d\,x}{2}-4\,B\,d\,x}{a^4\,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)}{a^4\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{111\,A}{8}-\frac{49\,B}{8}\right)}{a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{13\,A}{8}-\frac{23\,B}{24}\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{9\,A}{40}-\frac{7\,B}{40}\right)}{a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{A}{56}-\frac{B}{56}\right)}{a^4\,d}","Not used",1,"((21*A*d*x)/2 - 4*B*d*x)/(a^4*d) - (tan(c/2 + (d*x)/2)^3*(9*A - 2*B) + tan(c/2 + (d*x)/2)*(7*A - 2*B))/(a^4*d*(tan(c/2 + (d*x)/2)^2 + 1)^2) - (tan(c/2 + (d*x)/2)*((111*A)/8 - (49*B)/8))/(a^4*d) + (tan(c/2 + (d*x)/2)^3*((13*A)/8 - (23*B)/24))/(a^4*d) - (tan(c/2 + (d*x)/2)^5*((9*A)/40 - (7*B)/40))/(a^4*d) + (tan(c/2 + (d*x)/2)^7*(A/56 - B/56))/(a^4*d)","B"
117,1,300,256,2.049803,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + a/cos(c + d*x))^4,x)","\frac{\left(26\,A-9\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{124\,A}{3}-16\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(18\,A-7\,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)}^6+3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{x\,\left(44\,A-21\,B\right)}{2\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,\left(A-B\right)}{12\,a^4}+\frac{7\,A-5\,B}{6\,a^4}+\frac{21\,A-9\,B}{24\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A-B}{10\,a^4}+\frac{7\,A-5\,B}{40\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A-B\right)}{2\,a^4}+\frac{5\,\left(7\,A-5\,B\right)}{4\,a^4}+\frac{21\,A-9\,B}{2\,a^4}+\frac{35\,A-5\,B}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(26*A - 9*B) + tan(c/2 + (d*x)/2)^3*((124*A)/3 - 16*B) + tan(c/2 + (d*x)/2)*(18*A - 7*B))/(d*(3*a^4*tan(c/2 + (d*x)/2)^2 + 3*a^4*tan(c/2 + (d*x)/2)^4 + a^4*tan(c/2 + (d*x)/2)^6 + a^4)) - (x*(44*A - 21*B))/(2*a^4) - (tan(c/2 + (d*x)/2)^3*((5*(A - B))/(12*a^4) + (7*A - 5*B)/(6*a^4) + (21*A - 9*B)/(24*a^4)))/d + (tan(c/2 + (d*x)/2)^5*((A - B)/(10*a^4) + (7*A - 5*B)/(40*a^4)))/d + (tan(c/2 + (d*x)/2)*((5*(A - B))/(2*a^4) + (5*(7*A - 5*B))/(4*a^4) + (21*A - 9*B)/(2*a^4) + (35*A - 5*B)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4*d)","B"
118,1,512,187,10.046993,"\text{Not used}","int(((A + B/cos(c + d*x))*(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}}{5\,d}+\frac{\left(48\,A-32\,B\right)\,1{}\mathrm{i}}{105\,d}\right)+\frac{\left(336\,A+672\,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)}^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{B\,320{}\mathrm{i}}{63\,d}\right)+\frac{B\,32{}\mathrm{i}}{7\,d}+\frac{\left(144\,A+288\,B\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\,B\right)\,1{}\mathrm{i}}{9\,d}\right)+\frac{\left(16\,A+32\,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{{\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\,A+256\,B\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\,A+128\,B\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)*((A*16i)/(5*d) + ((48*A - 32*B)*1i)/(105*d)) + ((336*A + 672*B)*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)*((A*16i)/(7*d) - (B*320i)/(63*d)) + (B*32i)/(7*d) + ((144*A + 288*B)*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*B)*1i)/(9*d)) - (A*16i)/(9*d) + ((16*A + 32*B)*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*A + 256*B)*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*A + 128*B)*1i)/(315*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
119,1,407,144,6.163342,"\text{Not used}","int(((A + B/cos(c + d*x))*(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(-\frac{A\,8{}\mathrm{i}}{5\,d}+\frac{B\,16{}\mathrm{i}}{5\,d}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(\frac{B\,16{}\mathrm{i}}{35\,d}+\frac{\left(56\,A+112\,B\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{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\,B\right)\,1{}\mathrm{i}}{7\,d}\right)-\frac{\left(8\,A+16\,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{\left(\frac{A\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(56\,A+48\,B\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\,A+96\,B\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)*((B*16i)/(5*d) - (A*8i)/(5*d) + exp(c*1i + d*x*1i)*((B*16i)/(35*d) + ((56*A + 112*B)*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)*((A*8i)/(7*d) + exp(c*1i + d*x*1i)*((A*8i)/(7*d) - ((8*A + 16*B)*1i)/(7*d)) - ((8*A + 16*B)*1i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + (((A*8i)/(3*d) - (exp(c*1i + d*x*1i)*(56*A + 48*B)*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*A + 96*B)*1i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
120,1,212,101,6.157918,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^2,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(A\,5{}\mathrm{i}+B\,4{}\mathrm{i}+A\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,5{}\mathrm{i}+A\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,10{}\mathrm{i}+A\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,5{}\mathrm{i}+A\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,5{}\mathrm{i}+B\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,4{}\mathrm{i}+B\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,14{}\mathrm{i}+B\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,4{}\mathrm{i}+B\,{\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)*(A*5i + B*4i + A*exp(c*1i + d*x*1i)*5i + A*exp(c*2i + d*x*2i)*10i + A*exp(c*3i + d*x*3i)*5i + A*exp(c*4i + d*x*4i)*5i + B*exp(c*1i + d*x*1i)*4i + B*exp(c*2i + d*x*2i)*14i + B*exp(c*3i + d*x*3i)*4i + B*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"
121,1,159,62,1.966245,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x),x)","\frac{2\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(6\,A\,\sin\left(c+d\,x\right)+6\,B\,\sin\left(c+d\,x\right)+6\,A\,\sin\left(2\,c+2\,d\,x\right)+6\,A\,\sin\left(3\,c+3\,d\,x\right)+3\,A\,\sin\left(4\,c+4\,d\,x\right)+8\,B\,\sin\left(2\,c+2\,d\,x\right)+6\,B\,\sin\left(3\,c+3\,d\,x\right)+2\,B\,\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*A*sin(c + d*x) + 6*B*sin(c + d*x) + 6*A*sin(2*c + 2*d*x) + 6*A*sin(3*c + 3*d*x) + 3*A*sin(4*c + 4*d*x) + 8*B*sin(2*c + 2*d*x) + 6*B*sin(3*c + 3*d*x) + 2*B*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"
122,0,-1,66,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2), x)","F"
123,0,-1,68,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
124,0,-1,117,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
125,0,-1,160,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
126,0,-1,203,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
127,1,596,189,9.603537,"\text{Not used}","int(((A + B/cos(c + d*x))*(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\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(A+4\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{B\,a\,32{}\mathrm{i}}{63\,d}\right)+\frac{A\,a\,8{}\mathrm{i}}{7\,d}-\frac{a\,\left(A+2\,B\right)\,24{}\mathrm{i}}{7\,d}-\frac{B\,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(2\,A+3\,B\right)\,16{}\mathrm{i}}{9\,d}+\frac{a\,\left(3\,A+2\,B\right)\,8{}\mathrm{i}}{9\,d}+\frac{A\,a\,8{}\mathrm{i}}{9\,d}\right)+\frac{a\,\left(2\,A+3\,B\right)\,16{}\mathrm{i}}{9\,d}-\frac{a\,\left(3\,A+2\,B\right)\,8{}\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{\left(\frac{A\,a\,8{}\mathrm{i}}{3\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(39\,A+34\,B\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\,A+2\,B\right)\,8{}\mathrm{i}}{5\,d}+\frac{a\,\left(3\,A+B\right)\,16{}\mathrm{i}}{105\,d}\right)-\frac{A\,a\,8{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+3\,B\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\,A+34\,B\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)*((a*(A + 4*B)*8i)/(7*d) - (a*(3*A + 2*B)*8i)/(7*d) + (B*a*32i)/(63*d)) + (A*a*8i)/(7*d) - (a*(A + 2*B)*24i)/(7*d) - (B*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*(3*A + 2*B)*8i)/(9*d) - (a*(2*A + 3*B)*16i)/(9*d) + (A*a*8i)/(9*d)) + (a*(2*A + 3*B)*16i)/(9*d) - (a*(3*A + 2*B)*8i)/(9*d) - (A*a*8i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) + (((A*a*8i)/(3*d) - (a*exp(c*1i + d*x*1i)*(39*A + 34*B)*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*A + 2*B)*8i)/(5*d) + (a*(3*A + B)*16i)/(105*d)) - (A*a*8i)/(5*d) + (a*(A + 3*B)*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*A + 34*B)*16i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
128,1,479,138,6.888856,"\text{Not used}","int(((A + B/cos(c + d*x))*(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(7\,A+13\,B\right)\,8{}\mathrm{i}}{105\,d}-\frac{A\,a\,4{}\mathrm{i}}{3\,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\,\left(2\,A+3\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{7\,d}+\frac{A\,a\,4{}\mathrm{i}}{7\,d}\right)-\frac{a\,\left(2\,A+3\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{a\,\left(3\,A+2\,B\right)\,4{}\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\,a\,4{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+2\,B\right)\,12{}\mathrm{i}}{5\,d}+\frac{B\,a\,16{}\mathrm{i}}{35\,d}\right)-\frac{a\,\left(3\,A+2\,B\right)\,4{}\mathrm{i}}{5\,d}+\frac{a\,\left(A+4\,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{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\,A+52\,B\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*A + 2*B)*4i)/(7*d) - (a*(2*A + 3*B)*8i)/(7*d) + (A*a*4i)/(7*d)) - (a*(2*A + 3*B)*8i)/(7*d) + (a*(3*A + 2*B)*4i)/(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*(7*A + 13*B)*8i)/(105*d) - (A*a*4i)/(3*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 + 2*B)*12i)/(5*d) - (A*a*4i)/(5*d) + (B*a*16i)/(35*d)) - (a*(3*A + 2*B)*4i)/(5*d) + (a*(A + 4*B)*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*A + 52*B)*4i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
129,1,213,101,5.877037,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x),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(A\,25{}\mathrm{i}+B\,18{}\mathrm{i}+A\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,10{}\mathrm{i}+A\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,50{}\mathrm{i}+A\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,10{}\mathrm{i}+A\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,25{}\mathrm{i}+B\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,18{}\mathrm{i}+B\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,48{}\mathrm{i}+B\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,18{}\mathrm{i}+B\,{\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)*(A*25i + B*18i + A*exp(c*1i + d*x*1i)*10i + A*exp(c*2i + d*x*2i)*50i + A*exp(c*3i + d*x*3i)*10i + A*exp(c*4i + d*x*4i)*25i + B*exp(c*1i + d*x*1i)*18i + B*exp(c*2i + d*x*2i)*48i + B*exp(c*3i + d*x*3i)*18i + B*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"
130,0,-1,105,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
131,0,-1,103,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
132,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
133,0,-1,164,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
134,0,-1,209,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2), x)","F"
135,1,856,237,13.506484,"\text{Not used}","int(((A + B/cos(c + d*x))*(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(803\,A+710\,B\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\,A+2\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,A+16\,B\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(11\,A+50\,B\right)\,32{}\mathrm{i}}{693\,d}\right)+\frac{A\,a^2\,24{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(9\,A+10\,B\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\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(3\,A+4\,B\right)\,40{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(11\,A+10\,B\right)\,8{}\mathrm{i}}{11\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{11\,d}+\frac{a^2\,\left(3\,A+4\,B\right)\,40{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{11\,d}-\frac{a^2\,\left(11\,A+10\,B\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{B\,a^2\,64{}\mathrm{i}}{99\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,8{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,A+9\,B\right)\,16{}\mathrm{i}}{9\,d}\right)+\frac{A\,a^2\,8{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(A+2\,B\right)\,40{}\mathrm{i}}{9\,d}+\frac{B\,a^2\,64{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(A+B\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\,A+2\,B\right)\,8{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(44\,A-31\,B\right)\,16{}\mathrm{i}}{1155\,d}\right)-\frac{A\,a^2\,8{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(4\,A+5\,B\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\,A+710\,B\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)*((A*a^2*8i)/(3*d) - (a^2*exp(c*1i + d*x*1i)*(803*A + 710*B)*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)*((A*a^2*24i)/(7*d) - exp(c*1i + d*x*1i)*((a^2*(5*A + 16*B)*8i)/(7*d) - (a^2*(5*A + 2*B)*8i)/(7*d) + (a^2*(11*A + 50*B)*32i)/(693*d)) + (a^2*(9*A + 10*B)*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)*((A*a^2*8i)/(11*d) + (a^2*(3*A + 4*B)*40i)/(11*d) - (a^2*(5*A + 2*B)*8i)/(11*d) - (a^2*(11*A + 10*B)*8i)/(11*d)) + (A*a^2*8i)/(11*d) + (a^2*(3*A + 4*B)*40i)/(11*d) - (a^2*(5*A + 2*B)*8i)/(11*d) - (a^2*(11*A + 10*B)*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)*((A*a^2*8i)/(9*d) - exp(c*1i + d*x*1i)*((a^2*(A - 8*B)*8i)/(9*d) - (B*a^2*64i)/(99*d) + (a^2*(5*A + 2*B)*8i)/(9*d) - (a^2*(5*A + 9*B)*16i)/(9*d)) + (a^2*(A + 2*B)*40i)/(9*d) + (B*a^2*64i)/(9*d) - (a^2*(A + B)*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*A + 2*B)*8i)/(5*d) + (a^2*(44*A - 31*B)*16i)/(1155*d)) - (A*a^2*8i)/(5*d) + (a^2*(4*A + 5*B)*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*A + 710*B)*16i)/(3465*d*(exp(c*1i + d*x*1i) + 1))","B"
136,1,723,175,10.814921,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\frac{\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(60\,A+73\,B\right)\,8{}\mathrm{i}}{315\,d}\right)+\frac{a^2\,\left(5\,A+2\,B\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{A\,a^2\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(3\,A+4\,B\right)\,16{}\mathrm{i}}{105\,d}+\frac{a^2\,\left(9\,A+10\,B\right)\,4{}\mathrm{i}}{5\,d}\right)-\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(5\,A+16\,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}}{7\,d}+\frac{a^2\,\left(A+2\,B\right)\,20{}\mathrm{i}}{7\,d}+\frac{B\,a^2\,32{}\mathrm{i}}{63\,d}-\frac{a^2\,\left(A+B\right)\,40{}\mathrm{i}}{7\,d}\right)+\frac{a^2\,\left(A-8\,B\right)\,4{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+9\,B\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\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(3\,A+4\,B\right)\,20{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(11\,A+10\,B\right)\,4{}\mathrm{i}}{9\,d}\right)-\frac{A\,a^2\,4{}\mathrm{i}}{9\,d}-\frac{a^2\,\left(3\,A+4\,B\right)\,20{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(5\,A+2\,B\right)\,4{}\mathrm{i}}{9\,d}+\frac{a^2\,\left(11\,A+10\,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{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\,A+292\,B\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)*((A*a^2*4i)/(3*d) - (a^2*(60*A + 73*B)*8i)/(315*d)) + (a^2*(5*A + 2*B)*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*A + 4*B)*16i)/(105*d) - (A*a^2*4i)/(5*d) + (a^2*(9*A + 10*B)*4i)/(5*d)) - (a^2*(5*A + 2*B)*4i)/(5*d) + (a^2*(5*A + 16*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)/(7*d) + (a^2*(A + 2*B)*20i)/(7*d) + (B*a^2*32i)/(63*d) - (a^2*(A + B)*40i)/(7*d)) + (a^2*(A - 8*B)*4i)/(7*d) + (a^2*(5*A + 2*B)*4i)/(7*d) - (a^2*(5*A + 9*B)*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)*((A*a^2*4i)/(9*d) + (a^2*(3*A + 4*B)*20i)/(9*d) - (a^2*(5*A + 2*B)*4i)/(9*d) - (a^2*(11*A + 10*B)*4i)/(9*d)) - (A*a^2*4i)/(9*d) - (a^2*(3*A + 4*B)*20i)/(9*d) + (a^2*(5*A + 2*B)*4i)/(9*d) + (a^2*(11*A + 10*B)*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*A + 292*B)*4i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
137,1,590,138,6.347725,"\text{Not used}","int(((A + B/cos(c + d*x))*(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(301\,A+230\,B\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\,a^2\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(3\,A+4\,B\right)\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(11\,A+10\,B\right)\,2{}\mathrm{i}}{7\,d}\right)+\frac{A\,a^2\,2{}\mathrm{i}}{7\,d}+\frac{a^2\,\left(3\,A+4\,B\right)\,10{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(5\,A+2\,B\right)\,2{}\mathrm{i}}{7\,d}-\frac{a^2\,\left(11\,A+10\,B\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\,A+2\,B\right)\,2{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(5\,A+9\,B\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,\left(7\,A-8\,B\right)\,2{}\mathrm{i}}{35\,d}\right)-\frac{A\,a^2\,2{}\mathrm{i}}{5\,d}-\frac{a^2\,\left(A+2\,B\right)\,2{}\mathrm{i}}{d}+\frac{a^2\,\left(A+B\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\,A+2\,B\right)\,2{}\mathrm{i}}{3\,d}-\frac{a^2\,\left(63\,A+80\,B\right)\,2{}\mathrm{i}}{105\,d}\right)-\frac{A\,a^2\,2{}\mathrm{i}}{3\,d}+\frac{a^2\,\left(9\,A+10\,B\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^2*2i)/d - (a^2*exp(c*1i + d*x*1i)*(301*A + 230*B)*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*a^2*2i)/(7*d) + (a^2*(3*A + 4*B)*10i)/(7*d) - (a^2*(5*A + 2*B)*2i)/(7*d) - (a^2*(11*A + 10*B)*2i)/(7*d)) + (A*a^2*2i)/(7*d) + (a^2*(3*A + 4*B)*10i)/(7*d) - (a^2*(5*A + 2*B)*2i)/(7*d) - (a^2*(11*A + 10*B)*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*A + 2*B)*2i)/(5*d) - (a^2*(5*A + 9*B)*4i)/(5*d) + (a^2*(7*A - 8*B)*2i)/(35*d)) - (A*a^2*2i)/(5*d) - (a^2*(A + 2*B)*2i)/d + (a^2*(A + B)*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*A + 2*B)*2i)/(3*d) - (a^2*(63*A + 80*B)*2i)/(105*d)) - (A*a^2*2i)/(3*d) + (a^2*(9*A + 10*B)*2i)/(3*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
138,0,-1,142,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(5/2), x)","F"
139,0,-1,143,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(5/2), x)","F"
140,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(5/2), x)","F"
141,0,-1,164,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2), x)","F"
142,0,-1,209,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2), x)","F"
143,0,-1,254,0.000000,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^5\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2), x)","F"
144,0,-1,202,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/2)), x)","F"
145,0,-1,159,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/2)), x)","F"
146,0,-1,118,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/2)), x)","F"
147,0,-1,78,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/2)), x)","F"
148,0,-1,91,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{B}{\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))/(a + a/cos(c + d*x))^(1/2), x)","F"
149,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
150,0,-1,165,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
151,0,-1,206,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
152,0,-1,216,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)), x)","F"
153,0,-1,171,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(3/2)), x)","F"
154,0,-1,118,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(3/2)), x)","F"
155,0,-1,87,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(a + a/cos(c + d*x))^(3/2)), x)","F"
156,0,-1,127,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{B}{\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))/(a + a/cos(c + d*x))^(3/2), x)","F"
157,0,-1,170,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(3/2), x)","F"
158,0,-1,221,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(3/2), x)","F"
159,0,-1,268,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(3/2), x)","F"
160,0,-1,216,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)), x)","F"
161,0,-1,169,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)), x)","F"
162,0,-1,126,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/2)), x)","F"
163,0,-1,126,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/2)), x)","F"
164,0,-1,164,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{B}{\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))/(a + a/cos(c + d*x))^(5/2), x)","F"
165,0,-1,207,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(5/2), x)","F"
166,0,-1,264,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(5/2), x)","F"
167,0,-1,89,0.000000,"\text{Not used}","int((A + A/cos(c + d*x))/(a - a/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{A}{\cos\left(c+d\,x\right)}}{\sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + A/cos(c + d*x))/(a - a/cos(c + d*x))^(1/2), x)","F"
168,0,-1,115,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\right)}{\sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(1/2), x)","F"
169,0,-1,155,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\right)}{\sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(1/2), x)","F"
170,0,-1,192,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\right)}{\sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(1/2), x)","F"
171,0,-1,116,0.000000,"\text{Not used}","int((A + A/cos(c + d*x))/(a - a/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{A}{\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 + A/cos(c + d*x))/(a - a/cos(c + d*x))^(3/2), x)","F"
172,0,-1,146,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\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 + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(3/2), x)","F"
173,0,-1,194,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\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 + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(3/2), x)","F"
174,0,-1,236,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\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 + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(3/2), x)","F"
175,0,-1,152,0.000000,"\text{Not used}","int((A + A/cos(c + d*x))/(a - a/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{A}{\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 + A/cos(c + d*x))/(a - a/cos(c + d*x))^(5/2), x)","F"
176,0,-1,184,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\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 + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(5/2), x)","F"
177,0,-1,236,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\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 + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(5/2), x)","F"
178,0,-1,280,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+\frac{A}{\cos\left(c+d\,x\right)}\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 + A/cos(c + d*x)))/(a - a/cos(c + d*x))^(5/2), x)","F"
179,0,-1,199,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2), x)","F"
180,0,-1,172,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2), x)","F"
181,0,-1,135,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2), x)","F"
182,0,-1,106,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(1/2), x)","F"
183,0,-1,110,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(3/2), x)","F"
184,0,-1,141,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(5/2), x)","F"
185,0,-1,172,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x)))/(1/cos(c + d*x))^(7/2), x)","F"
186,0,-1,234,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2), x)","F"
187,0,-1,199,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2), x)","F"
188,0,-1,160,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/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{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))*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2), x)","F"
189,0,-1,158,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/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{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))*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2), x)","F"
190,0,-1,166,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/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{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))*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(5/2), x)","F"
191,0,-1,201,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/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{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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(7/2), x)","F"
192,0,-1,234,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/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{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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^2)/(1/cos(c + d*x))^(9/2), x)","F"
193,0,-1,277,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2), x)","F"
194,0,-1,244,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2), x)","F"
195,0,-1,211,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2), x)","F"
196,0,-1,199,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2), x)","F"
197,0,-1,211,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(5/2), x)","F"
198,0,-1,211,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(7/2), x)","F"
199,0,-1,244,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(9/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(9/2), x)","F"
200,0,-1,277,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(11/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^3)/(1/cos(c + d*x))^(11/2), x)","F"
201,0,-1,229,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x)), x)","F"
202,0,-1,192,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x)), x)","F"
203,0,-1,153,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x)), x)","F"
204,0,-1,123,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x)), x)","F"
205,0,-1,128,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
206,0,-1,164,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
207,0,-1,197,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)), x)","F"
208,0,-1,230,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(7/2)), x)","F"
209,0,-1,237,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\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))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^2, x)","F"
210,0,-1,204,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^2, x)","F"
211,0,-1,161,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^2, x)","F"
212,0,-1,168,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^2, x)","F"
213,0,-1,177,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
214,0,-1,211,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
215,0,-1,244,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)), x)","F"
216,0,-1,292,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + a/cos(c + d*x))^3, x)","F"
217,0,-1,261,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^3, x)","F"
218,0,-1,220,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^3, x)","F"
219,0,-1,216,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^3, x)","F"
220,0,-1,222,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^3, x)","F"
221,0,-1,228,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
222,0,-1,261,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
223,0,-1,294,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)), x)","F"
224,0,-1,176,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2), x)","F"
225,0,-1,131,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2), x)","F"
226,0,-1,78,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2), x)","F"
227,0,-1,76,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
228,1,81,82,2.785327,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),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(4\,A\,\sin\left(c+d\,x\right)+6\,B\,\sin\left(c+d\,x\right)+A\,\sin\left(2\,c+2\,d\,x\right)\right)}{3\,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)*(4*A*sin(c + d*x) + 6*B*sin(c + d*x) + A*sin(2*c + 2*d*x)))/(3*d*(cos(c + d*x) + 1))","B"
229,1,106,130,3.379555,"\text{Not used}","int(((A + B/cos(c + d*x))*(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)+40\,B\,\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) + 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"
230,1,130,175,4.188451,"\text{Not used}","int(((A + B/cos(c + d*x))*(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)+490\,B\,\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)\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) + 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)))/(420*d*(cos(c + d*x) + 1))","B"
231,0,-1,227,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2), x)","F"
232,0,-1,180,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2), x)","F"
233,0,-1,133,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2), x)","F"
234,0,-1,124,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{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))*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
235,0,-1,125,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{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))*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2), x)","F"
236,1,107,131,3.404881,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(5/2),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(75\,A\,\sin\left(c+d\,x\right)+100\,B\,\sin\left(c+d\,x\right)+18\,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,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(75*A*sin(c + d*x) + 100*B*sin(c + d*x) + 18*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"
237,1,131,181,4.338208,"\text{Not used}","int(((A + B/cos(c + d*x))*(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)+1050\,B\,\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)\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) + 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)))/(420*d*(cos(c + d*x) + 1))","B"
238,1,155,228,5.299472,"\text{Not used}","int(((A + B/cos(c + d*x))*(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)+5460\,B\,\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)\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) + 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)))/(2520*d*(cos(c + d*x) + 1))","B"
239,0,-1,274,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2), x)","F"
240,0,-1,227,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2), x)","F"
241,0,-1,180,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2), x)","F"
242,0,-1,180,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{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))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
243,0,-1,177,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{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))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)","F"
244,0,-1,172,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{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))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(5/2), x)","F"
245,1,133,178,4.346820,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(7/2),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(1960\,A\,\sin\left(c+d\,x\right)+2450\,B\,\sin\left(c+d\,x\right)+490\,A\,\sin\left(2\,c+2\,d\,x\right)+120\,A\,\sin\left(3\,c+3\,d\,x\right)+15\,A\,\sin\left(4\,c+4\,d\,x\right)+392\,B\,\sin\left(2\,c+2\,d\,x\right)+42\,B\,\sin\left(3\,c+3\,d\,x\right)\right)}{420\,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)*(1960*A*sin(c + d*x) + 2450*B*sin(c + d*x) + 490*A*sin(2*c + 2*d*x) + 120*A*sin(3*c + 3*d*x) + 15*A*sin(4*c + 4*d*x) + 392*B*sin(2*c + 2*d*x) + 42*B*sin(3*c + 3*d*x)))/(420*d*(cos(c + d*x) + 1))","B"
246,1,157,228,5.548734,"\text{Not used}","int(((A + B/cos(c + d*x))*(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)+11760\,B\,\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)\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) + 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)))/(2520*d*(cos(c + d*x) + 1))","B"
247,1,392,275,8.768343,"\text{Not used}","int(((A + B/cos(c + d*x))*(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{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{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}+\frac{a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(13\,A+10\,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)}{56\,d}+\frac{a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(19\,A+20\,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)}{12\,d}+\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,A+26\,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)}{4\,d}+\frac{a^2\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(25\,A+24\,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)}{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*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((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) + (a^2*sin((7*c)/2 + (7*d*x)/2)*(13*A + 10*B)*(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 + 20*B)*(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 + 26*B)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(4*d) + (a^2*sin((5*c)/2 + (5*d*x)/2)*(25*A + 24*B)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(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"
248,0,-1,190,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(1/2), x)","F"
249,0,-1,141,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(1/2), x)","F"
250,0,-1,100,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(1/2), x)","F"
251,0,-1,99,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
252,0,-1,142,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
253,0,-1,187,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
254,0,-1,230,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/2)), x)","F"
255,0,-1,247,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^(3/2), x)","F"
256,0,-1,197,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(3/2), x)","F"
257,0,-1,145,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(3/2), x)","F"
258,0,-1,107,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(3/2), x)","F"
259,0,-1,156,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
260,0,-1,203,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
261,0,-1,250,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
262,0,-1,246,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\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))*(1/cos(c + d*x))^(7/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
263,0,-1,194,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
264,0,-1,156,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\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{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
265,0,-1,156,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a/cos(c + d*x))^(5/2), x)","F"
266,0,-1,203,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
267,0,-1,250,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
268,0,-1,297,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)), x)","F"
269,0,-1,406,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(2/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + a/cos(c + d*x))^(2/3), x)","F"
270,0,-1,354,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(a + a/cos(c + d*x))^(1/3), x)","F"
271,0,-1,415,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^(4/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(a + a/cos(c + d*x))^(4/3), x)","F"
272,0,-1,787,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(4/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + a/cos(c + d*x))^(4/3), x)","F"
273,0,-1,739,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + a/cos(c + d*x))^(1/3), x)","F"
274,0,-1,764,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + a/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(a + a/cos(c + d*x))^(2/3), x)","F"
275,0,-1,197,0.000000,"\text{Not used}","int((A + B/cos(e + f*x))*(a + a/cos(e + f*x))^m*(c/cos(e + f*x))^n,x)","\int \left(A+\frac{B}{\cos\left(e+f\,x\right)}\right)\,{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((A + B/cos(e + f*x))*(a + a/cos(e + f*x))^m*(c/cos(e + f*x))^n, x)","F"
276,0,-1,164,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^n)/(1/cos(c + d*x))^(n + 1),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^n)/(1/cos(c + d*x))^(n + 1), x)","F"
277,1,194,114,5.726742,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{\left(A\,a-2\,A\,b-2\,B\,a+\frac{5\,B\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{10\,A\,b}{3}-A\,a+\frac{10\,B\,a}{3}+\frac{3\,B\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,B\,b}{4}-\frac{10\,A\,b}{3}-\frac{10\,B\,a}{3}-A\,a\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}\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(A\,a+\frac{3\,B\,b}{4}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A*a + 2*A*b + 2*B*a + (5*B*b)/4) + tan(c/2 + (d*x)/2)^7*(A*a - 2*A*b - 2*B*a + (5*B*b)/4) - tan(c/2 + (d*x)/2)^3*(A*a + (10*A*b)/3 + (10*B*a)/3 - (3*B*b)/4) + tan(c/2 + (d*x)/2)^5*((10*A*b)/3 - A*a + (10*B*a)/3 + (3*B*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))*(A*a + (3*B*b)/4))/d","B"
278,1,145,93,4.385261,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A\,b+B\,a\right)}{d}-\frac{\left(2\,A\,a-A\,b-B\,a+2\,B\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a-\frac{4\,B\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+A\,b+B\,a+2\,B\,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))*(A*b + B*a))/d - (tan(c/2 + (d*x)/2)*(2*A*a + A*b + B*a + 2*B*b) - tan(c/2 + (d*x)/2)^3*(4*A*a + (4*B*b)/3) + tan(c/2 + (d*x)/2)^5*(2*A*a - A*b - B*a + 2*B*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"
279,1,104,61,3.142824,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/cos(c + d*x),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b+2\,B\,a+B\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,b+2\,B\,a-B\,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\,A\,a+B\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*b + 2*B*a + B*b) - tan(c/2 + (d*x)/2)^3*(2*A*b + 2*B*a - B*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*A*a + B*b))/d","B"
280,1,114,35,2.243990,"\text{Not used}","int((A + B/cos(c + d*x))*(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{B\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\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{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}","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 - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (B*b*sin(c + d*x))/(d*cos(c + d*x))","B"
281,1,100,35,2.191005,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(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\,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}","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*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","B"
282,1,50,52,2.034196,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x)),x)","\frac{A\,a\,x}{2}+B\,b\,x+\frac{A\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*a*x)/2 + B*b*x + (A*b*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (A*a*sin(2*c + 2*d*x))/(4*d)","B"
283,1,84,84,2.067292,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x)),x)","\frac{A\,b\,x}{2}+\frac{B\,a\,x}{2}+\frac{3\,A\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b\,\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 + (3*A*a*sin(c + d*x))/(4*d) + (B*b*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"
284,1,117,105,2.125563,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + b/cos(c + d*x)),x)","\frac{3\,A\,a\,x}{8}+\frac{B\,b\,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{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}","Not used",1,"(3*A*a*x)/8 + (B*b*x)/2 + (3*A*b*sin(c + d*x))/(4*d) + (3*B*a*sin(c + d*x))/(4*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)","B"
285,1,359,198,5.706550,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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}{2}+\frac{3\,B\,a\,b}{4}+\frac{3\,A\,b^2}{8}\right)}{2\,A\,a^2+3\,B\,a\,b+\frac{3\,A\,b^2}{2}}\right)\,\left(A\,a^2+\frac{3\,B\,a\,b}{2}+\frac{3\,A\,b^2}{4}\right)}{d}-\frac{\left(2\,B\,a^2-\frac{5\,A\,b^2}{4}-A\,a^2+2\,B\,b^2+4\,A\,a\,b-\frac{5\,B\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,a^2+\frac{A\,b^2}{2}-\frac{16\,B\,a^2}{3}-\frac{8\,B\,b^2}{3}-\frac{32\,A\,a\,b}{3}+B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,B\,a^2}{3}+\frac{40\,A\,a\,b}{3}+\frac{116\,B\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-2\,A\,a^2-\frac{A\,b^2}{2}-\frac{16\,B\,a^2}{3}-\frac{8\,B\,b^2}{3}-\frac{32\,A\,a\,b}{3}-B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a^2+\frac{5\,A\,b^2}{4}+2\,B\,a^2+2\,B\,b^2+4\,A\,a\,b+\frac{5\,B\,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)*((A*a^2)/2 + (3*A*b^2)/8 + (3*B*a*b)/4))/(2*A*a^2 + (3*A*b^2)/2 + 3*B*a*b))*(A*a^2 + (3*A*b^2)/4 + (3*B*a*b)/2))/d - (tan(c/2 + (d*x)/2)^5*((20*B*a^2)/3 + (116*B*b^2)/15 + (40*A*a*b)/3) - tan(c/2 + (d*x)/2)^9*(A*a^2 + (5*A*b^2)/4 - 2*B*a^2 - 2*B*b^2 - 4*A*a*b + (5*B*a*b)/2) - tan(c/2 + (d*x)/2)^3*(2*A*a^2 + (A*b^2)/2 + (16*B*a^2)/3 + (8*B*b^2)/3 + (32*A*a*b)/3 + B*a*b) + tan(c/2 + (d*x)/2)^7*(2*A*a^2 + (A*b^2)/2 - (16*B*a^2)/3 - (8*B*b^2)/3 - (32*A*a*b)/3 + B*a*b) + tan(c/2 + (d*x)/2)*(A*a^2 + (5*A*b^2)/4 + 2*B*a^2 + 2*B*b^2 + 4*A*a*b + (5*B*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"
286,1,317,179,5.686990,"\text{Not used}","int(((A + B/cos(c + d*x))*(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}+A\,a\,b+\frac{3\,B\,b^2}{8}\right)}{2\,B\,a^2+4\,A\,a\,b+\frac{3\,B\,b^2}{2}}\right)\,\left(B\,a^2+2\,A\,a\,b+\frac{3\,B\,b^2}{4}\right)}{d}-\frac{\left(2\,A\,a^2+2\,A\,b^2-B\,a^2-\frac{5\,B\,b^2}{4}-2\,A\,a\,b+4\,B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(B\,a^2-\frac{10\,A\,b^2}{3}-6\,A\,a^2-\frac{3\,B\,b^2}{4}+2\,A\,a\,b-\frac{20\,B\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,a^2+\frac{10\,A\,b^2}{3}+B\,a^2-\frac{3\,B\,b^2}{4}+2\,A\,a\,b+\frac{20\,B\,a\,b}{3}\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\,A\,a\,b-4\,B\,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)*((B*a^2)/2 + (3*B*b^2)/8 + A*a*b))/(2*B*a^2 + (3*B*b^2)/2 + 4*A*a*b))*(B*a^2 + (3*B*b^2)/4 + 2*A*a*b))/d - (tan(c/2 + (d*x)/2)^7*(2*A*a^2 + 2*A*b^2 - B*a^2 - (5*B*b^2)/4 - 2*A*a*b + 4*B*a*b) + tan(c/2 + (d*x)/2)^3*(6*A*a^2 + (10*A*b^2)/3 + B*a^2 - (3*B*b^2)/4 + 2*A*a*b + (20*B*a*b)/3) - tan(c/2 + (d*x)/2)^5*(6*A*a^2 + (10*A*b^2)/3 - B*a^2 + (3*B*b^2)/4 - 2*A*a*b + (20*B*a*b)/3) - tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 + (5*B*b^2)/4 + 2*A*a*b + 4*B*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"
287,1,227,116,5.444464,"\text{Not used}","int(((A + B/cos(c + d*x))*(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(A\,a^2+B\,a\,b+\frac{A\,b^2}{2}\right)}{4\,A\,a^2+4\,B\,a\,b+2\,A\,b^2}\right)\,\left(2\,A\,a^2+2\,B\,a\,b+A\,b^2\right)}{d}-\frac{\left(2\,B\,a^2-A\,b^2+2\,B\,b^2+4\,A\,a\,b-2\,B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,B\,a^2-8\,A\,a\,b-\frac{4\,B\,b^2}{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+4\,A\,a\,b+2\,B\,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)*(A*a^2 + (A*b^2)/2 + B*a*b))/(4*A*a^2 + 2*A*b^2 + 4*B*a*b))*(2*A*a^2 + A*b^2 + 2*B*a*b))/d - (tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 + 4*A*a*b + 2*B*a*b) - tan(c/2 + (d*x)/2)^3*(4*B*a^2 + (4*B*b^2)/3 + 8*A*a*b) + tan(c/2 + (d*x)/2)^5*(2*B*a^2 - A*b^2 + 2*B*b^2 + 4*A*a*b - 2*B*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"
288,1,176,86,2.737114,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\frac{2\,\left(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)+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)+\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)}{2}+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)\right)}{d}+\frac{\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,b^2\,\sin\left(c+d\,x\right)}{2}+B\,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*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 2*A*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((A*b^2*sin(2*c + 2*d*x))/2 + (B*b^2*sin(c + d*x))/2 + B*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
289,1,163,60,2.546689,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\frac{B\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{d}+\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{2\,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)}{d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}+\frac{4\,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\,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)}{d}","Not used",1,"(B*b^2*tan(c + d*x))/d + (2*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*b^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*cos(c + d*x)) + (4*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*B*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
290,1,169,80,2.381383,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d}+\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)}{d}+\frac{2\,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}+\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{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{d}+\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}","Not used",1,"(B*a^2*sin(c + d*x))/d + (A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*b^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 + (A*a^2*sin(2*c + 2*d*x))/(4*d) + (2*A*a*b*sin(c + d*x))/d + (4*B*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
291,1,115,107,2.101093,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\frac{B\,a^2\,x}{2}+B\,b^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}+A\,a\,b\,x+\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{A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(B*a^2*x)/2 + B*b^2*x + (3*A*a^2*sin(c + d*x))/(4*d) + (A*b^2*sin(c + d*x))/d + A*a*b*x + (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 + (A*a*b*sin(2*c + 2*d*x))/(2*d)","B"
292,1,169,136,2.183254,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\frac{3\,A\,a^2\,x}{8}+\frac{A\,b^2\,x}{2}+\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{3\,A\,a\,b\,\sin\left(c+d\,x\right)}{2\,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 + (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) + (3*A*a*b*sin(c + d*x))/(2*d) + (A*a*b*sin(3*c + 3*d*x))/(6*d) + (B*a*b*sin(2*c + 2*d*x))/(2*d)","B"
293,1,307,180,5.808274,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\frac{x\,\left(\frac{3\,B\,a^2}{4}+\frac{3\,A\,a\,b}{2}+B\,b^2\right)}{2}+\frac{\left(2\,A\,a^2+2\,A\,b^2-\frac{5\,B\,a^2}{4}-B\,b^2-\frac{5\,A\,a\,b}{2}+4\,B\,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{B\,a^2}{2}-2\,B\,b^2-A\,a\,b+\frac{32\,B\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^2}{15}+\frac{40\,B\,a\,b}{3}+\frac{20\,A\,b^2}{3}\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{B\,a^2}{2}+2\,B\,b^2+A\,a\,b+\frac{32\,B\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+\frac{5\,B\,a^2}{4}+B\,b^2+\frac{5\,A\,a\,b}{2}+4\,B\,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*B*a^2)/4 + B*b^2 + (3*A*a*b)/2))/2 + (tan(c/2 + (d*x)/2)^5*((116*A*a^2)/15 + (20*A*b^2)/3 + (40*B*a*b)/3) + tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 - (5*B*a^2)/4 - B*b^2 - (5*A*a*b)/2 + 4*B*a*b) + tan(c/2 + (d*x)/2)^3*((8*A*a^2)/3 + (16*A*b^2)/3 + (B*a^2)/2 + 2*B*b^2 + A*a*b + (32*B*a*b)/3) + tan(c/2 + (d*x)/2)^7*((8*A*a^2)/3 + (16*A*b^2)/3 - (B*a^2)/2 - 2*B*b^2 - A*a*b + (32*B*a*b)/3) + tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + (5*B*a^2)/4 + B*b^2 + (5*A*a*b)/2 + 4*B*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"
294,1,470,252,5.786506,"\text{Not used}","int(((A + B/cos(c + d*x))*(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{3\,A\,a^2\,b}{2}+\frac{9\,B\,a\,b^2}{8}+\frac{3\,A\,b^3}{8}\right)}{2\,B\,a^3+6\,A\,a^2\,b+\frac{9\,B\,a\,b^2}{2}+\frac{3\,A\,b^3}{2}}\right)\,\left(B\,a^3+3\,A\,a^2\,b+\frac{9\,B\,a\,b^2}{4}+\frac{3\,A\,b^3}{4}\right)}{d}-\frac{\left(2\,A\,a^3-\frac{5\,A\,b^3}{4}-B\,a^3+2\,B\,b^3+6\,A\,a\,b^2-3\,A\,a^2\,b-\frac{15\,B\,a\,b^2}{4}+6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b^3}{2}-8\,A\,a^3+2\,B\,a^3-\frac{8\,B\,b^3}{3}-16\,A\,a\,b^2+6\,A\,a^2\,b+\frac{3\,B\,a\,b^2}{2}-16\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,A\,a^3+20\,B\,a^2\,b+20\,A\,a\,b^2+\frac{116\,B\,b^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,A\,a^3-\frac{A\,b^3}{2}-2\,B\,a^3-\frac{8\,B\,b^3}{3}-16\,A\,a\,b^2-6\,A\,a^2\,b-\frac{3\,B\,a\,b^2}{2}-16\,B\,a^2\,b\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+6\,A\,a\,b^2+3\,A\,a^2\,b+\frac{15\,B\,a\,b^2}{4}+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)}^{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*A*b^3)/8 + (B*a^3)/2 + (3*A*a^2*b)/2 + (9*B*a*b^2)/8))/((3*A*b^3)/2 + 2*B*a^3 + 6*A*a^2*b + (9*B*a*b^2)/2))*((3*A*b^3)/4 + B*a^3 + 3*A*a^2*b + (9*B*a*b^2)/4))/d - (tan(c/2 + (d*x)/2)*(2*A*a^3 + (5*A*b^3)/4 + B*a^3 + 2*B*b^3 + 6*A*a*b^2 + 3*A*a^2*b + (15*B*a*b^2)/4 + 6*B*a^2*b) + tan(c/2 + (d*x)/2)^5*(12*A*a^3 + (116*B*b^3)/15 + 20*A*a*b^2 + 20*B*a^2*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^3 - (5*A*b^3)/4 - B*a^3 + 2*B*b^3 + 6*A*a*b^2 - 3*A*a^2*b - (15*B*a*b^2)/4 + 6*B*a^2*b) - tan(c/2 + (d*x)/2)^3*(8*A*a^3 + (A*b^3)/2 + 2*B*a^3 + (8*B*b^3)/3 + 16*A*a*b^2 + 6*A*a^2*b + (3*B*a*b^2)/2 + 16*B*a^2*b) - tan(c/2 + (d*x)/2)^7*(8*A*a^3 - (A*b^3)/2 - 2*B*a^3 + (8*B*b^3)/3 + 16*A*a*b^2 - 6*A*a^2*b - (3*B*a*b^2)/2 + 16*B*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"
295,1,395,180,6.014637,"\text{Not used}","int(((A + B/cos(c + d*x))*(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(A\,a^3+\frac{3\,B\,a^2\,b}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,b^3}{8}\right)}{4\,A\,a^3+6\,B\,a^2\,b+6\,A\,a\,b^2+\frac{3\,B\,b^3}{2}}\right)\,\left(2\,A\,a^3+3\,B\,a^2\,b+3\,A\,a\,b^2+\frac{3\,B\,b^3}{4}\right)}{d}-\frac{\left(2\,A\,b^3+2\,B\,a^3-\frac{5\,B\,b^3}{4}-3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(3\,A\,a\,b^2-6\,B\,a^3-\frac{3\,B\,b^3}{4}-\frac{10\,A\,b^3}{3}-18\,A\,a^2\,b-10\,B\,a\,b^2+3\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{10\,A\,b^3}{3}+6\,B\,a^3-\frac{3\,B\,b^3}{4}+3\,A\,a\,b^2+18\,A\,a^2\,b+10\,B\,a\,b^2+3\,B\,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}-3\,A\,a\,b^2-6\,A\,a^2\,b-6\,B\,a\,b^2-3\,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)}^8-4\,{\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*a^3 + (3*B*b^3)/8 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2))/(4*A*a^3 + (3*B*b^3)/2 + 6*A*a*b^2 + 6*B*a^2*b))*(2*A*a^3 + (3*B*b^3)/4 + 3*A*a*b^2 + 3*B*a^2*b))/d - (tan(c/2 + (d*x)/2)^7*(2*A*b^3 + 2*B*a^3 - (5*B*b^3)/4 - 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 - 3*B*a^2*b) + tan(c/2 + (d*x)/2)^3*((10*A*b^3)/3 + 6*B*a^3 - (3*B*b^3)/4 + 3*A*a*b^2 + 18*A*a^2*b + 10*B*a*b^2 + 3*B*a^2*b) - tan(c/2 + (d*x)/2)^5*((10*A*b^3)/3 + 6*B*a^3 + (3*B*b^3)/4 - 3*A*a*b^2 + 18*A*a^2*b + 10*B*a*b^2 - 3*B*a^2*b) - tan(c/2 + (d*x)/2)*(2*A*b^3 + 2*B*a^3 + (5*B*b^3)/4 + 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 + 3*B*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"
296,1,526,137,4.026107,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3,x)","\frac{\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{B\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,A\,a\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,B\,a^2\,b\,\sin\left(c+d\,x\right)}{4}+\frac{3\,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{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}}{4}-\frac{B\,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\,A\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,B\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,B\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4}+\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)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{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}}{4}-\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(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}-\frac{A\,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{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)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{4}-\frac{A\,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{B\,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*b^3*sin(2*c + 2*d*x))/4 + (B*b^3*sin(3*c + 3*d*x))/6 + (B*b^3*sin(c + d*x))/2 + (3*A*a*b^2*sin(c + d*x))/4 + (3*B*a^2*b*sin(c + d*x))/4 + (3*A*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (A*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 - (B*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 + (3*A*a*b^2*sin(3*c + 3*d*x))/4 + (3*B*a*b^2*sin(2*c + 2*d*x))/4 + (3*B*a^2*b*sin(3*c + 3*d*x))/4 + (A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (A*b^3*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*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 - (A*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 - (B*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 - (A*a^2*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2 - (B*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"
297,1,249,119,3.598212,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3,x)","\frac{\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{B\,b^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,B\,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(-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)+\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)\,1{}\mathrm{i}}{2}-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)+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)\,3{}\mathrm{i}+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)\,3{}\mathrm{i}\right)}{d}","Not used",1,"((A*a^3*sin(3*c + 3*d*x))/4 + (A*b^3*sin(2*c + 2*d*x))/2 + (A*a^3*sin(c + d*x))/4 + (B*b^3*sin(c + d*x))/2 + (3*B*a*b^2*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*((B*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2 - B*a^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)) + A*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i + B*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i))/d","B"
298,1,236,124,3.334516,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3,x)","\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)-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)\,2{}\mathrm{i}+6\,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)+6\,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)\,6{}\mathrm{i}}{d}+\frac{\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{8}+B\,b^3\,\sin\left(c+d\,x\right)+\frac{3\,A\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - A*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 6*A*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*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))*6i)/d + ((A*a^3*sin(3*c + 3*d*x))/8 + (B*a^3*sin(2*c + 2*d*x))/2 + (A*a^3*sin(c + d*x))/8 + B*b^3*sin(c + d*x) + (3*A*a^2*b*sin(2*c + 2*d*x))/2)/(d*cos(c + d*x))","B"
299,1,1924,145,3.902037,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3,x)","\frac{\left(2\,A\,a^3-B\,a^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(\frac{4\,A\,a^3}{3}+12\,B\,a^2\,b+12\,A\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+B\,a^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)}^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}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)\,1{}\mathrm{i}-\left(\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)\,1{}\mathrm{i}}{\left(\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)+\left(\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)\right)\,\left(\frac{1{}\mathrm{i}\,B\,a^3}{2}+\frac{3{}\mathrm{i}\,A\,a^2\,b}{2}+3{}\mathrm{i}\,B\,a\,b^2+1{}\mathrm{i}\,A\,b^3\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+384\,A\,B^2\,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}\right)\,\left(B\,a^3+3\,A\,a^2\,b+6\,B\,a\,b^2+2\,A\,b^3\right)}{d}-\frac{B\,b^3\,\mathrm{atan}\left(\frac{B\,b^3\,\left(\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)+B\,b^3\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\right)\right)\,1{}\mathrm{i}+B\,b^3\,\left(\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)-B\,b^3\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\right)\right)\,1{}\mathrm{i}}{64\,A^2\,B\,b^9-64\,A\,B^2\,b^9-192\,B^3\,a\,b^8+B\,b^3\,\left(\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)+B\,b^3\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\right)\right)-B\,b^3\,\left(\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+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6\right)-B\,b^3\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2\right)\right)+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+384\,A\,B^2\,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}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^3 + B*a^3 + 6*A*a*b^2 + 3*A*a^2*b + 6*B*a^2*b) + tan(c/2 + (d*x)/2)^3*((4*A*a^3)/3 + 12*A*a*b^2 + 12*B*a^2*b) + tan(c/2 + (d*x)/2)^5*(2*A*a^3 - B*a^3 + 6*A*a*b^2 - 3*A*a^2*b + 6*B*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((((A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2) + 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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3))*(A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i)*1i - ((A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2) - 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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3))*(A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i)*1i)/(((A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2) + 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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3))*(A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i) + ((A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2) - 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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3))*(A*b^3*1i + (B*a^3*1i)/2 + (A*a^2*b*3i)/2 + B*a*b^2*3i) - 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 + 384*A*B^2*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))*(2*A*b^3 + B*a^3 + 3*A*a^2*b + 6*B*a*b^2))/d - (B*b^3*atan((B*b^3*(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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3) + B*b^3*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2))*1i + B*b^3*(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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3) - B*b^3*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2))*1i)/(64*A^2*B*b^9 - 64*A*B^2*b^9 - 192*B^3*a*b^8 + B*b^3*(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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3) + B*b^3*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2)) - B*b^3*(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 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 320*A*B*a^3*b^3) - B*b^3*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2)) + 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 + 384*A*B^2*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))*2i)/d","B"
300,1,202,179,2.489874,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3,x)","\frac{3\,A\,a^3\,x}{8}+B\,b^3\,x+\frac{3\,A\,a\,b^2\,x}{2}+\frac{3\,B\,a^2\,b\,x}{2}+\frac{A\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,A\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{9\,A\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*A*a^3*x)/8 + B*b^3*x + (3*A*a*b^2*x)/2 + (3*B*a^2*b*x)/2 + (A*b^3*sin(c + d*x))/d + (3*B*a^3*sin(c + d*x))/(4*d) + (A*a^3*sin(2*c + 2*d*x))/(4*d) + (A*a^3*sin(4*c + 4*d*x))/(32*d) + (B*a^3*sin(3*c + 3*d*x))/(12*d) + (3*A*a*b^2*sin(2*c + 2*d*x))/(4*d) + (A*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*B*a^2*b*sin(2*c + 2*d*x))/(4*d) + (9*A*a^2*b*sin(c + d*x))/(4*d) + (3*B*a*b^2*sin(c + d*x))/d","B"
301,1,277,221,2.728431,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3,x)","\frac{A\,b^3\,x}{2}+\frac{3\,B\,a^3\,x}{8}+\frac{9\,A\,a^2\,b\,x}{8}+\frac{3\,B\,a\,b^2\,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{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{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{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}","Not used",1,"(A*b^3*x)/2 + (3*B*a^3*x)/8 + (9*A*a^2*b*x)/8 + (3*B*a*b^2*x)/2 + (5*A*a^3*sin(c + d*x))/(8*d) + (B*b^3*sin(c + d*x))/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) + (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) + (9*A*a*b^2*sin(c + d*x))/(4*d) + (9*B*a^2*b*sin(c + d*x))/(4*d)","B"
302,1,709,334,5.737417,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4)/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}+2\,A\,a^3\,b+\frac{9\,B\,a^2\,b^2}{4}+\frac{3\,A\,a\,b^3}{2}+\frac{5\,B\,b^4}{16}\right)}{2\,B\,a^4+8\,A\,a^3\,b+9\,B\,a^2\,b^2+6\,A\,a\,b^3+\frac{5\,B\,b^4}{4}}\right)\,\left(B\,a^4+4\,A\,a^3\,b+\frac{9\,B\,a^2\,b^2}{2}+3\,A\,a\,b^3+\frac{5\,B\,b^4}{8}\right)}{d}+\frac{\left(B\,a^4-2\,A\,b^4-2\,A\,a^4+\frac{11\,B\,b^4}{8}-12\,A\,a^2\,b^2+\frac{15\,B\,a^2\,b^2}{2}+5\,A\,a\,b^3+4\,A\,a^3\,b-8\,B\,a\,b^3-8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(10\,A\,a^4+\frac{14\,A\,b^4}{3}-3\,B\,a^4+\frac{5\,B\,b^4}{24}+44\,A\,a^2\,b^2-\frac{21\,B\,a^2\,b^2}{2}-7\,A\,a\,b^3-12\,A\,a^3\,b+\frac{56\,B\,a\,b^3}{3}+\frac{88\,B\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,B\,a^4-\frac{52\,A\,b^4}{5}-20\,A\,a^4+\frac{15\,B\,b^4}{4}-72\,A\,a^2\,b^2+3\,B\,a^2\,b^2+2\,A\,a\,b^3+8\,A\,a^3\,b-\frac{208\,B\,a\,b^3}{5}-48\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(20\,A\,a^4+\frac{52\,A\,b^4}{5}+2\,B\,a^4+\frac{15\,B\,b^4}{4}+72\,A\,a^2\,b^2+3\,B\,a^2\,b^2+2\,A\,a\,b^3+8\,A\,a^3\,b+\frac{208\,B\,a\,b^3}{5}+48\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,B\,b^4}{24}-\frac{14\,A\,b^4}{3}-3\,B\,a^4-10\,A\,a^4-44\,A\,a^2\,b^2-\frac{21\,B\,a^2\,b^2}{2}-7\,A\,a\,b^3-12\,A\,a^3\,b-\frac{56\,B\,a\,b^3}{3}-\frac{88\,B\,a^3\,b}{3}\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}+12\,A\,a^2\,b^2+\frac{15\,B\,a^2\,b^2}{2}+5\,A\,a\,b^3+4\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,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)}","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))/(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))*(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))/d + (tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + B*a^4 + (11*B*b^4)/8 + 12*A*a^2*b^2 + (15*B*a^2*b^2)/2 + 5*A*a*b^3 + 4*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b) - tan(c/2 + (d*x)/2)^11*(2*A*a^4 + 2*A*b^4 - B*a^4 - (11*B*b^4)/8 + 12*A*a^2*b^2 - (15*B*a^2*b^2)/2 - 5*A*a*b^3 - 4*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b) - tan(c/2 + (d*x)/2)^3*(10*A*a^4 + (14*A*b^4)/3 + 3*B*a^4 - (5*B*b^4)/24 + 44*A*a^2*b^2 + (21*B*a^2*b^2)/2 + 7*A*a*b^3 + 12*A*a^3*b + (56*B*a*b^3)/3 + (88*B*a^3*b)/3) + tan(c/2 + (d*x)/2)^9*(10*A*a^4 + (14*A*b^4)/3 - 3*B*a^4 + (5*B*b^4)/24 + 44*A*a^2*b^2 - (21*B*a^2*b^2)/2 - 7*A*a*b^3 - 12*A*a^3*b + (56*B*a*b^3)/3 + (88*B*a^3*b)/3) + tan(c/2 + (d*x)/2)^5*(20*A*a^4 + (52*A*b^4)/5 + 2*B*a^4 + (15*B*b^4)/4 + 72*A*a^2*b^2 + 3*B*a^2*b^2 + 2*A*a*b^3 + 8*A*a^3*b + (208*B*a*b^3)/5 + 48*B*a^3*b) - tan(c/2 + (d*x)/2)^7*(20*A*a^4 + (52*A*b^4)/5 - 2*B*a^4 - (15*B*b^4)/4 + 72*A*a^2*b^2 - 3*B*a^2*b^2 - 2*A*a*b^3 - 8*A*a^3*b + (208*B*a*b^3)/5 + 48*B*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))","B"
303,1,555,250,6.014324,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4)/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^4+2\,B\,a^3\,b+3\,A\,a^2\,b^2+\frac{3\,B\,a\,b^3}{2}+\frac{3\,A\,b^4}{8}\right)}{4\,A\,a^4+8\,B\,a^3\,b+12\,A\,a^2\,b^2+6\,B\,a\,b^3+\frac{3\,A\,b^4}{2}}\right)\,\left(2\,A\,a^4+4\,B\,a^3\,b+6\,A\,a^2\,b^2+3\,B\,a\,b^3+\frac{3\,A\,b^4}{4}\right)}{d}-\frac{\left(2\,B\,a^4-\frac{5\,A\,b^4}{4}+2\,B\,b^4-6\,A\,a^2\,b^2+12\,B\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b-5\,B\,a\,b^3-4\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b^4}{2}-8\,B\,a^4-\frac{8\,B\,b^4}{3}+12\,A\,a^2\,b^2-32\,B\,a^2\,b^2-\frac{64\,A\,a\,b^3}{3}-32\,A\,a^3\,b+2\,B\,a\,b^3+8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,B\,a^4+48\,A\,a^3\,b+40\,B\,a^2\,b^2+\frac{80\,A\,a\,b^3}{3}+\frac{116\,B\,b^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{A\,b^4}{2}-8\,B\,a^4-\frac{8\,B\,b^4}{3}-12\,A\,a^2\,b^2-32\,B\,a^2\,b^2-\frac{64\,A\,a\,b^3}{3}-32\,A\,a^3\,b-2\,B\,a\,b^3-8\,B\,a^3\,b\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+6\,A\,a^2\,b^2+12\,B\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b+5\,B\,a\,b^3+4\,B\,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)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*(A*a^4 + (3*A*b^4)/8 + 3*A*a^2*b^2 + (3*B*a*b^3)/2 + 2*B*a^3*b))/(4*A*a^4 + (3*A*b^4)/2 + 12*A*a^2*b^2 + 6*B*a*b^3 + 8*B*a^3*b))*(2*A*a^4 + (3*A*b^4)/4 + 6*A*a^2*b^2 + 3*B*a*b^3 + 4*B*a^3*b))/d - (tan(c/2 + (d*x)/2)*((5*A*b^4)/4 + 2*B*a^4 + 2*B*b^4 + 6*A*a^2*b^2 + 12*B*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b + 5*B*a*b^3 + 4*B*a^3*b) + tan(c/2 + (d*x)/2)^5*(12*B*a^4 + (116*B*b^4)/15 + 40*B*a^2*b^2 + (80*A*a*b^3)/3 + 48*A*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*B*a^4 - (5*A*b^4)/4 + 2*B*b^4 - 6*A*a^2*b^2 + 12*B*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b - 5*B*a*b^3 - 4*B*a^3*b) - tan(c/2 + (d*x)/2)^3*((A*b^4)/2 + 8*B*a^4 + (8*B*b^4)/3 + 12*A*a^2*b^2 + 32*B*a^2*b^2 + (64*A*a*b^3)/3 + 32*A*a^3*b + 2*B*a*b^3 + 8*B*a^3*b) - tan(c/2 + (d*x)/2)^7*(8*B*a^4 - (A*b^4)/2 + (8*B*b^4)/3 - 12*A*a^2*b^2 + 32*B*a^2*b^2 + (64*A*a*b^3)/3 + 32*A*a^3*b - 2*B*a*b^3 - 8*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))","B"
304,1,1969,200,5.005923,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","\frac{9\,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{27\,B\,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}+4\,A\,b^4\,\sin\left(2\,c+2\,d\,x\right)+A\,b^4\,\sin\left(4\,c+4\,d\,x\right)+\frac{9\,B\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+9\,A\,a^4\,\mathrm{atan}\left(\frac{64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^8+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+512\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+1792\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+96\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^8+1024\,A^2\,a^6\,b^2+1024\,A^2\,a^4\,b^4+256\,A^2\,a^2\,b^6+512\,A\,B\,a^7\,b+1792\,A\,B\,a^5\,b^3+960\,A\,B\,a^3\,b^5+96\,A\,B\,a\,b^7+64\,B^2\,a^8+384\,B^2\,a^6\,b^2+624\,B^2\,a^4\,b^4+144\,B^2\,a^2\,b^6+9\,B^2\,b^8\right)}\right)+\frac{33\,B\,b^4\,\sin\left(c+d\,x\right)}{8}+12\,A\,a^4\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^8+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+512\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+1792\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+96\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^8+1024\,A^2\,a^6\,b^2+1024\,A^2\,a^4\,b^4+256\,A^2\,a^2\,b^6+512\,A\,B\,a^7\,b+1792\,A\,B\,a^5\,b^3+960\,A\,B\,a^3\,b^5+96\,A\,B\,a\,b^7+64\,B^2\,a^8+384\,B^2\,a^6\,b^2+624\,B^2\,a^4\,b^4+144\,B^2\,a^2\,b^6+9\,B^2\,b^8\right)}\right)+3\,A\,a^4\,\cos\left(4\,c+4\,d\,x\right)\,\mathrm{atan}\left(\frac{64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^8+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+512\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+1792\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+96\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^8+1024\,A^2\,a^6\,b^2+1024\,A^2\,a^4\,b^4+256\,A^2\,a^2\,b^6+512\,A\,B\,a^7\,b+1792\,A\,B\,a^5\,b^3+960\,A\,B\,a^3\,b^5+96\,A\,B\,a\,b^7+64\,B^2\,a^8+384\,B^2\,a^6\,b^2+624\,B^2\,a^4\,b^4+144\,B^2\,a^2\,b^6+9\,B^2\,b^8\right)}\right)+6\,A\,a\,b^3\,\sin\left(c+d\,x\right)+18\,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)+36\,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)+6\,A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)+16\,B\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+12\,B\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+4\,B\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)+6\,B\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)+9\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)+12\,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)+3\,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)+27\,B\,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\,B\,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\,B\,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}+18\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)+9\,A\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)+9\,B\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)+24\,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(2\,c+2\,d\,x\right)+48\,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(2\,c+2\,d\,x\right)+6\,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(4\,c+4\,d\,x\right)+12\,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(4\,c+4\,d\,x\right)+36\,B\,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\,B\,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*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (27*B*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + 4*A*b^4*sin(2*c + 2*d*x) + A*b^4*sin(4*c + 4*d*x) + (9*B*b^4*sin(3*c + 3*d*x))/8 + 9*A*a^4*atan((64*A^2*a^8*sin(c/2 + (d*x)/2) + 64*B^2*a^8*sin(c/2 + (d*x)/2) + 9*B^2*b^8*sin(c/2 + (d*x)/2) + 256*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 1024*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*B^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*B^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*B^2*a^6*b^2*sin(c/2 + (d*x)/2) + 960*A*B*a^3*b^5*sin(c/2 + (d*x)/2) + 1792*A*B*a^5*b^3*sin(c/2 + (d*x)/2) + 96*A*B*a*b^7*sin(c/2 + (d*x)/2) + 512*A*B*a^7*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(64*A^2*a^8 + 64*B^2*a^8 + 9*B^2*b^8 + 256*A^2*a^2*b^6 + 1024*A^2*a^4*b^4 + 1024*A^2*a^6*b^2 + 144*B^2*a^2*b^6 + 624*B^2*a^4*b^4 + 384*B^2*a^6*b^2 + 96*A*B*a*b^7 + 512*A*B*a^7*b + 960*A*B*a^3*b^5 + 1792*A*B*a^5*b^3))) + (33*B*b^4*sin(c + d*x))/8 + 12*A*a^4*cos(2*c + 2*d*x)*atan((64*A^2*a^8*sin(c/2 + (d*x)/2) + 64*B^2*a^8*sin(c/2 + (d*x)/2) + 9*B^2*b^8*sin(c/2 + (d*x)/2) + 256*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 1024*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*B^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*B^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*B^2*a^6*b^2*sin(c/2 + (d*x)/2) + 960*A*B*a^3*b^5*sin(c/2 + (d*x)/2) + 1792*A*B*a^5*b^3*sin(c/2 + (d*x)/2) + 96*A*B*a*b^7*sin(c/2 + (d*x)/2) + 512*A*B*a^7*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(64*A^2*a^8 + 64*B^2*a^8 + 9*B^2*b^8 + 256*A^2*a^2*b^6 + 1024*A^2*a^4*b^4 + 1024*A^2*a^6*b^2 + 144*B^2*a^2*b^6 + 624*B^2*a^4*b^4 + 384*B^2*a^6*b^2 + 96*A*B*a*b^7 + 512*A*B*a^7*b + 960*A*B*a^3*b^5 + 1792*A*B*a^5*b^3))) + 3*A*a^4*cos(4*c + 4*d*x)*atan((64*A^2*a^8*sin(c/2 + (d*x)/2) + 64*B^2*a^8*sin(c/2 + (d*x)/2) + 9*B^2*b^8*sin(c/2 + (d*x)/2) + 256*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 1024*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*B^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*B^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*B^2*a^6*b^2*sin(c/2 + (d*x)/2) + 960*A*B*a^3*b^5*sin(c/2 + (d*x)/2) + 1792*A*B*a^5*b^3*sin(c/2 + (d*x)/2) + 96*A*B*a*b^7*sin(c/2 + (d*x)/2) + 512*A*B*a^7*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(64*A^2*a^8 + 64*B^2*a^8 + 9*B^2*b^8 + 256*A^2*a^2*b^6 + 1024*A^2*a^4*b^4 + 1024*A^2*a^6*b^2 + 144*B^2*a^2*b^6 + 624*B^2*a^4*b^4 + 384*B^2*a^6*b^2 + 96*A*B*a*b^7 + 512*A*B*a^7*b + 960*A*B*a^3*b^5 + 1792*A*B*a^5*b^3))) + 6*A*a*b^3*sin(c + d*x) + 18*A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 36*A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*A*a*b^3*sin(3*c + 3*d*x) + 16*B*a*b^3*sin(2*c + 2*d*x) + 12*B*a^3*b*sin(2*c + 2*d*x) + 4*B*a*b^3*sin(4*c + 4*d*x) + 6*B*a^3*b*sin(4*c + 4*d*x) + 9*B*a^2*b^2*sin(c + d*x) + 12*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 3*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 27*B*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (9*B*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (9*B*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8 + 18*A*a^2*b^2*sin(2*c + 2*d*x) + 9*A*a^2*b^2*sin(4*c + 4*d*x) + 9*B*a^2*b^2*sin(3*c + 3*d*x) + 24*A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 48*A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 6*A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 12*A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 36*B*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 9*B*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"
305,1,636,195,4.902441,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","\frac{\frac{A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{B\,b^4\,\sin\left(c+d\,x\right)}{2}+A\,a\,b^3\,\sin\left(c+d\,x\right)+\frac{3\,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)}{2}-\frac{A\,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}+A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)+B\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2}+\frac{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)}{2}-\frac{A\,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{3\,B\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+2\,A\,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)-A\,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}-B\,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}-B\,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)\,2{}\mathrm{i}-A\,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}+6\,A\,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)-B\,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}-B\,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)\,6{}\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,"((A*a^4*sin(2*c + 2*d*x))/4 + (A*a^4*sin(4*c + 4*d*x))/8 + (A*b^4*sin(2*c + 2*d*x))/4 + (B*b^4*sin(3*c + 3*d*x))/6 + (B*b^4*sin(c + d*x))/2 + A*a*b^3*sin(c + d*x) + (3*B*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (A*b^4*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 + A*a*b^3*sin(3*c + 3*d*x) + B*a*b^3*sin(2*c + 2*d*x) + (3*B*a^2*b^2*sin(c + d*x))/2 + (B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (A*b^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/4 + (3*B*a^2*b^2*sin(3*c + 3*d*x))/2 + 2*A*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) - A*a^2*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i - B*a*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i - B*a^3*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*2i - A*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 + 6*A*a^3*b*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i - B*a^3*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
306,1,330,209,4.389759,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","\frac{2\,\left(\frac{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)}{2}+\frac{B\,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}+4\,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)+4\,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)+6\,A\,a^2\,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\,B\,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)\right)}{d}+\frac{\frac{A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{4}+\frac{B\,b^4\,\sin\left(c+d\,x\right)}{2}+A\,a^3\,b\,\sin\left(c+d\,x\right)+A\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)+2\,B\,a\,b^3\,\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*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (B*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 4*A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 4*B*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*A*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*B*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((A*a^4*sin(2*c + 2*d*x))/8 + (A*a^4*sin(4*c + 4*d*x))/16 + (A*b^4*sin(2*c + 2*d*x))/2 + (B*a^4*sin(3*c + 3*d*x))/4 + (B*a^4*sin(c + d*x))/4 + (B*b^4*sin(c + d*x))/2 + A*a^3*b*sin(c + d*x) + A*a^3*b*sin(3*c + 3*d*x) + 2*B*a*b^3*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
307,1,2523,198,4.308308,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","-\frac{\left(2\,A\,a^4-B\,a^4-2\,B\,b^4+12\,A\,a^2\,b^2-4\,A\,a^3\,b+8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(B\,a^4-\frac{2\,A\,a^4}{3}-6\,B\,b^4+12\,A\,a^2\,b^2+4\,A\,a^3\,b+8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{2\,A\,a^4}{3}+B\,a^4-6\,B\,b^4-12\,A\,a^2\,b^2+4\,A\,a^3\,b-8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,A\,a^4-B\,a^4-2\,B\,b^4-12\,A\,a^2\,b^2-4\,A\,a^3\,b-8\,B\,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)}^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(A\,b^4+4\,B\,a\,b^3\right)\,\left(\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\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+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\right)\right)\,1{}\mathrm{i}-\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\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+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\right)\right)\,1{}\mathrm{i}}{\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\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+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\right)\right)+\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(\left(A\,b^4+4\,B\,a\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\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+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\right)\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^3-7168\,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}\right)\,\left(2{}\mathrm{i}\,A\,b^4+8{}\mathrm{i}\,B\,a\,b^3\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+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\right)-\frac{a\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\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+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\right)+\frac{a\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\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^3-7168\,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-\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+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\right)-\frac{a\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\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+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\right)+\frac{a\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\right)\,\left(32\,A\,b^4+16\,B\,a^4+192\,B\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\right)\,1{}\mathrm{i}}{2}}\right)\,\left(B\,a^3+4\,A\,a^2\,b+12\,B\,a\,b^2+8\,A\,b^3\right)}{d}","Not used",1,"- (tan(c/2 + (d*x)/2)^7*(2*A*a^4 - B*a^4 - 2*B*b^4 + 12*A*a^2*b^2 - 4*A*a^3*b + 8*B*a^3*b) - tan(c/2 + (d*x)/2)*(2*A*a^4 + B*a^4 + 2*B*b^4 + 12*A*a^2*b^2 + 4*A*a^3*b + 8*B*a^3*b) + tan(c/2 + (d*x)/2)^3*((2*A*a^4)/3 + B*a^4 - 6*B*b^4 - 12*A*a^2*b^2 + 4*A*a^3*b - 8*B*a^3*b) + tan(c/2 + (d*x)/2)^5*(B*a^4 - (2*A*a^4)/3 - 6*B*b^4 + 12*A*a^2*b^2 + 4*A*a^3*b + 8*B*a^3*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(((A*b^4 + 4*B*a*b^3)*((A*b^4 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3))*1i - (A*b^4 + 4*B*a*b^3)*((A*b^4 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3))*1i)/((A*b^4 + 4*B*a*b^3)*((A*b^4 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3)) + (A*b^4 + 4*B*a*b^3)*((A*b^4 + 4*B*a*b^3)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*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 - 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))*(A*b^4*2i + 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 + 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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3) - (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2))/2 + (a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3) + (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2))/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 - (a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3) - (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2)*1i)/2 + (a*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^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 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3) + (a*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2)*(32*A*b^4 + 16*B*a^4 + 192*B*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3)*1i)/2)*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2)*1i)/2 - 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))*(8*A*b^3 + B*a^3 + 4*A*a^2*b + 12*B*a*b^2))/d","B"
308,1,369,216,3.384029,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","\frac{3\,B\,a^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,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{2\,A\,b^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\,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)}{d}+\frac{A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{B\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{8\,B\,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}+\frac{4\,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)}{d}+\frac{A\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{B\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{6\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{6\,A\,a^2\,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{3\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{4\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*B*a^4*sin(c + d*x))/(4*d) + (3*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (2*A*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^4*sin(2*c + 2*d*x))/(4*d) + (A*a^4*sin(4*c + 4*d*x))/(32*d) + (B*a^4*sin(3*c + 3*d*x))/(12*d) + (8*B*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*B*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^3*b*sin(3*c + 3*d*x))/(3*d) + (B*a^3*b*sin(2*c + 2*d*x))/d + (6*B*a^2*b^2*sin(c + d*x))/d + (6*A*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*A*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (4*A*a*b^3*sin(c + d*x))/d + (3*A*a^3*b*sin(c + d*x))/d","B"
309,1,307,258,2.713452,"\text{Not used}","int(cos(c + d*x)^5*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","\frac{3\,B\,a^4\,x}{8}+B\,b^4\,x+2\,A\,a\,b^3\,x+\frac{3\,A\,a^3\,b\,x}{2}+\frac{5\,A\,a^4\,\sin\left(c+d\,x\right)}{8\,d}+\frac{A\,b^4\,\sin\left(c+d\,x\right)}{d}+3\,B\,a^2\,b^2\,x+\frac{5\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{A\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{9\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{B\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2\,d}+\frac{3\,B\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{4\,B\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*B*a^4*x)/8 + B*b^4*x + 2*A*a*b^3*x + (3*A*a^3*b*x)/2 + (5*A*a^4*sin(c + d*x))/(8*d) + (A*b^4*sin(c + d*x))/d + 3*B*a^2*b^2*x + (5*A*a^4*sin(3*c + 3*d*x))/(48*d) + (A*a^4*sin(5*c + 5*d*x))/(80*d) + (B*a^4*sin(2*c + 2*d*x))/(4*d) + (B*a^4*sin(4*c + 4*d*x))/(32*d) + (A*a*b^3*sin(2*c + 2*d*x))/d + (A*a^3*b*sin(2*c + 2*d*x))/d + (A*a^3*b*sin(4*c + 4*d*x))/(8*d) + (9*A*a^2*b^2*sin(c + d*x))/(2*d) + (B*a^3*b*sin(3*c + 3*d*x))/(3*d) + (A*a^2*b^2*sin(3*c + 3*d*x))/(2*d) + (3*B*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (4*B*a*b^3*sin(c + d*x))/d + (3*B*a^3*b*sin(c + d*x))/d","B"
310,1,403,309,3.183163,"\text{Not used}","int(cos(c + d*x)^6*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4,x)","\frac{5\,A\,a^4\,x}{16}+\frac{A\,b^4\,x}{2}+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}+\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{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{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\,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}","Not used",1,"(5*A*a^4*x)/16 + (A*b^4*x)/2 + 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 + (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) + (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) + (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*A*a*b^3*sin(c + d*x))/d + (5*A*a^3*b*sin(c + d*x))/(2*d)","B"
311,1,4667,187,6.930974,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^4*(a + b/cos(c + d*x))),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^2+2\,B\,a^2+2\,B\,b^2-2\,A\,a\,b-B\,a\,b\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,B\,a^2-A\,b^2+2\,B\,b^2-2\,A\,a\,b+B\,a\,b\right)}{b^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,B\,a^2-3\,A\,a\,b+B\,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\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{b^{10}}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{2\,b^4}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,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\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{b^{10}}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{2\,b^4}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(-4\,A^3\,a^8\,b^3+6\,A^3\,a^7\,b^4-6\,A^3\,a^6\,b^5+5\,A^3\,a^5\,b^6-2\,A^3\,a^4\,b^7+A^3\,a^3\,b^8+12\,A^2\,B\,a^9\,b^2-18\,A^2\,B\,a^8\,b^3+18\,A^2\,B\,a^7\,b^4-15\,A^2\,B\,a^6\,b^5+6\,A^2\,B\,a^5\,b^6-3\,A^2\,B\,a^4\,b^7-12\,A\,B^2\,a^{10}\,b+18\,A\,B^2\,a^9\,b^2-18\,A\,B^2\,a^8\,b^3+15\,A\,B^2\,a^7\,b^4-6\,A\,B^2\,a^6\,b^5+3\,A\,B^2\,a^5\,b^6+4\,B^3\,a^{11}-6\,B^3\,a^{10}\,b+6\,B^3\,a^9\,b^2-5\,B^3\,a^8\,b^3+2\,B^3\,a^7\,b^4-B^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^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{b^{10}}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{2\,b^4}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{b^{10}}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{2\,b^4}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,b^3\right)}{2\,b^4}}\right)\,\left(-2\,B\,a^3+2\,A\,a^2\,b-B\,a\,b^2+A\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,a\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(-4\,A^3\,a^8\,b^3+6\,A^3\,a^7\,b^4-6\,A^3\,a^6\,b^5+5\,A^3\,a^5\,b^6-2\,A^3\,a^4\,b^7+A^3\,a^3\,b^8+12\,A^2\,B\,a^9\,b^2-18\,A^2\,B\,a^8\,b^3+18\,A^2\,B\,a^7\,b^4-15\,A^2\,B\,a^6\,b^5+6\,A^2\,B\,a^5\,b^6-3\,A^2\,B\,a^4\,b^7-12\,A\,B^2\,a^{10}\,b+18\,A\,B^2\,a^9\,b^2-18\,A\,B^2\,a^8\,b^3+15\,A\,B^2\,a^7\,b^4-6\,A\,B^2\,a^6\,b^5+3\,A\,B^2\,a^5\,b^6+4\,B^3\,a^{11}-6\,B^3\,a^{10}\,b+6\,B^3\,a^9\,b^2-5\,B^3\,a^8\,b^3+2\,B^3\,a^7\,b^4-B^3\,a^6\,b^5\right)}{b^9}+\frac{a^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 - 2*A*a*b - B*a*b))/b^3 + (tan(c/2 + (d*x)/2)^5*(2*B*a^2 - A*b^2 + 2*B*b^2 - 2*A*a*b + B*a*b))/b^3 - (4*tan(c/2 + (d*x)/2)^3*(3*B*a^2 + B*b^2 - 3*A*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)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - (((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*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)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/b^10)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/(2*b^4))*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + (((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*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)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/b^10)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/(2*b^4))*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2)*1i)/(2*b^4))/((16*(4*B^3*a^11 - 6*B^3*a^10*b + A^3*a^3*b^8 - 2*A^3*a^4*b^7 + 5*A^3*a^5*b^6 - 6*A^3*a^6*b^5 + 6*A^3*a^7*b^4 - 4*A^3*a^8*b^3 - B^3*a^6*b^5 + 2*B^3*a^7*b^4 - 5*B^3*a^8*b^3 + 6*B^3*a^9*b^2 - 12*A*B^2*a^10*b + 3*A*B^2*a^5*b^6 - 6*A*B^2*a^6*b^5 + 15*A*B^2*a^7*b^4 - 18*A*B^2*a^8*b^3 + 18*A*B^2*a^9*b^2 - 3*A^2*B*a^4*b^7 + 6*A^2*B*a^5*b^6 - 15*A^2*B*a^6*b^5 + 18*A^2*B*a^7*b^4 - 18*A^2*B*a^8*b^3 + 12*A^2*B*a^9*b^2))/b^9 - (((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - (((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*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)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/b^10)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/(2*b^4))*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + (((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*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)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/b^10)*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/(2*b^4))*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2))/(2*b^4)))*(A*b^3 - 2*B*a^3 + 2*A*a^2*b - B*a*b^2)*1i)/(b^4*d) - (a^3*atan(((a^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + (a^3*((a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + (a^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - (a^3*((a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(4*B^3*a^11 - 6*B^3*a^10*b + A^3*a^3*b^8 - 2*A^3*a^4*b^7 + 5*A^3*a^5*b^6 - 6*A^3*a^6*b^5 + 6*A^3*a^7*b^4 - 4*A^3*a^8*b^3 - B^3*a^6*b^5 + 2*B^3*a^7*b^4 - 5*B^3*a^8*b^3 + 6*B^3*a^9*b^2 - 12*A*B^2*a^10*b + 3*A*B^2*a^5*b^6 - 6*A*B^2*a^6*b^5 + 15*A*B^2*a^7*b^4 - 18*A*B^2*a^8*b^3 + 18*A*B^2*a^9*b^2 - 3*A^2*B*a^4*b^7 + 6*A^2*B*a^5*b^6 - 15*A^2*B*a^6*b^5 + 18*A^2*B*a^7*b^4 - 18*A^2*B*a^8*b^3 + 12*A^2*B*a^9*b^2))/b^9 + (a^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + (a^3*((a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) - (a^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - (a^3*((a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*((a + b)*(a - b))^(1/2)*(A*b - B*a)*2i)/(d*(b^6 - a^2*b^4))","B"
312,1,4047,143,6.083171,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^3*(a + b/cos(c + d*x))),x)","\frac{B\,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{A\,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{B\,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{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}}{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\,\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{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}}{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^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{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)\,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{A\,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{B\,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{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)\,\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{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)\,\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{B\,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{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)\,\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{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)\,\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{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)\,\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{A\,a^2\,\mathrm{atan}\left(\frac{\left(8\,B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-B^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,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}-4\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,A\,B\,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\,A^2\,a^4\,b^3+4\,A^2\,a^2\,b^5+4\,A\,B\,a^5\,b^2-4\,A\,B\,a\,b^6-3\,B^2\,a^4\,b^3+2\,B^2\,a^2\,b^5+B^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{B\,a^3\,\mathrm{atan}\left(\frac{\left(8\,B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-B^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,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}-4\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,A\,B\,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\,A^2\,a^4\,b^3+4\,A^2\,a^2\,b^5+4\,A\,B\,a^5\,b^2-4\,A\,B\,a\,b^6-3\,B^2\,a^4\,b^3+2\,B^2\,a^2\,b^5+B^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{A\,a^2\,\mathrm{atan}\left(\frac{\left(8\,B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-B^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,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}-4\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,A\,B\,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\,A^2\,a^4\,b^3+4\,A^2\,a^2\,b^5+4\,A\,B\,a^5\,b^2-4\,A\,B\,a\,b^6-3\,B^2\,a^4\,b^3+2\,B^2\,a^2\,b^5+B^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{B\,a^3\,\mathrm{atan}\left(\frac{\left(8\,B^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-8\,B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-B^2\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-4\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+12\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,B^2\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,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}-4\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-16\,A\,B\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}+16\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+4\,A\,B\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-20\,A\,B\,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\,A^2\,a^4\,b^3+4\,A^2\,a^2\,b^5+4\,A\,B\,a^5\,b^2-4\,A\,B\,a\,b^6-3\,B^2\,a^4\,b^3+2\,B^2\,a^2\,b^5+B^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,"(B*a*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*b*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b*sin(c + d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*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)) + (B*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)) + (A*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)) + (B*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)) - (B*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)) + (A*a^2*sin(2*c + 2*d*x))/(2*b*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*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)) - (A*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)) + (B*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)) + (B*a^2*sin(c + d*x))/(2*b*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (A*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)) + (B*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)) - (B*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)) + (A*a^2*atan(((8*B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*B^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + B^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - B^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*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) - 4*A*B*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*A*B*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*A*B*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)*(B^2*b^7 + 4*A^2*a^2*b^5 - 4*A^2*a^4*b^3 + 2*B^2*a^2*b^5 - 3*B^2*a^4*b^3 - 4*A*B*a*b^6 + 4*A*B*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)) - (B*a^3*atan(((8*B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*B^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + B^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - B^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*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) - 4*A*B*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*A*B*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*A*B*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)*(B^2*b^7 + 4*A^2*a^2*b^5 - 4*A^2*a^4*b^3 + 2*B^2*a^2*b^5 - 3*B^2*a^4*b^3 - 4*A*B*a*b^6 + 4*A*B*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)) + (A*a^2*atan(((8*B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*B^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + B^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - B^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*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) - 4*A*B*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*A*B*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*A*B*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)*(B^2*b^7 + 4*A^2*a^2*b^5 - 4*A^2*a^4*b^3 + 2*B^2*a^2*b^5 - 3*B^2*a^4*b^3 - 4*A*B*a*b^6 + 4*A*B*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)) - (B*a^3*atan(((8*B^2*a^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - 8*B^2*a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + B^2*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - B^2*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 4*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 12*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*B^2*a^3*b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*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) - 4*A*B*a*b^8*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 16*A*B*a^6*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) + 16*A*B*a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 4*A*B*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 20*A*B*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)*(B^2*b^7 + 4*A^2*a^2*b^5 - 4*A^2*a^4*b^3 + 2*B^2*a^2*b^5 - 3*B^2*a^4*b^3 - 4*A*B*a*b^6 + 4*A*B*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"
313,1,719,98,2.970759,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^2*(a + b/cos(c + d*x))),x)","\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\,\left(a^2-b^2\right)}-\frac{2\,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\,\left(a^2-b^2\right)}-\frac{B\,b\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}-\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{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)}{b\,d\,\left(a^2-b^2\right)}-\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)}{b^2\,d\,\left(a^2-b^2\right)}-\frac{A\,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{B\,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{A\,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\,a^2\,\mathrm{tan}\left(c+d\,x\right)}{b\,d\,\left(a^2-b^2\right)}-\frac{B\,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{A\,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*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (2*A*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (B*b*tan(c + d*x))/(d*(a^2 - b^2)) - (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)) + (2*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)) - (2*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d*(a^2 - b^2)) - (A*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)) + (B*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)) + (A*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*a^2*tan(c + d*x))/(b*d*(a^2 - b^2)) - (B*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)) + (A*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"
314,1,573,76,3.085048,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + b/cos(c + d*x))),x)","\frac{A\,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{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)}}{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{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\,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{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{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\,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,"(A*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)) - (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))/(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)) - (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*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*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)) + (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*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"
315,1,573,67,3.196251,"\text{Not used}","int((A + B/cos(c + d*x))/(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\,\left(a^2-b^2\right)}-\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{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\,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\,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)}{a\,d\,\left(a^2-b^2\right)}+\frac{A\,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{A\,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{A\,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*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^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)) + (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*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*A*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d*(a^2 - b^2)) + (A*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)) - (A*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)) + (A*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"
316,1,740,90,3.358767,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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^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\,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^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*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((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*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((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"
317,1,3740,134,6.018833,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(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{\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,a^9\,b\right)}{a^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,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}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)}{2\,a^3}+\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\,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\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,a^3}-\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,a^9\,b\right)}{a^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,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}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)}{2\,a^3}-\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\,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\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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^7-4\,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+4\,B^3\,a^4\,b^4-4\,B^3\,a^3\,b^5\right)}{a^6}+\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,a^9\,b\right)}{a^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,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}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)}{2\,a^3}+\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\,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\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)}{2\,a^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,a^9\,b\right)}{a^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,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}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)}{2\,a^3}-\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\,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\right)}{a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,b^2\right)}{2\,a^3}}\right)\,\left(1{}\mathrm{i}\,A\,a^2-2{}\mathrm{i}\,B\,a\,b+2{}\mathrm{i}\,A\,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(\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\,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\right)}{a^4}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,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(A\,b-B\,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)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{a^5-a^3\,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^7-3\,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\,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\right)}{a^4}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,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(A\,b-B\,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)\,\left(A\,b-B\,a\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^7-4\,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+4\,B^3\,a^4\,b^4-4\,B^3\,a^3\,b^5\right)}{a^6}+\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^7-3\,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\,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\right)}{a^4}+\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,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(A\,b-B\,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)\,\left(A\,b-B\,a\right)}{a^5-a^3\,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^7-3\,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\,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\right)}{a^4}-\frac{b^2\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,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^2-2\,A\,a^9\,b-4\,B\,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(A\,b-B\,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)\,\left(A\,b-B\,a\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 - (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*a^2*1i + A*b^2*2i - B*a*b*2i))/(2*a^3) + (8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4)*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*1i)/(2*a^3) - (((((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 + (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*a^2*1i + A*b^2*2i - B*a*b*2i))/(2*a^3) - (8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4)*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*1i)/(2*a^3))/((16*(4*A^3*b^8 - 6*A^3*a*b^7 + 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 - 12*A^2*B*a*b^7 + 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))/a^6 + (((((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 - (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*a^2*1i + A*b^2*2i - B*a*b*2i))/(2*a^3) + (8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4)*(A*a^2*1i + A*b^2*2i - B*a*b*2i))/(2*a^3) + (((((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 + (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*a^2*1i + A*b^2*2i - B*a*b*2i))/(2*a^3) - (8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4)*(A*a^2*1i + A*b^2*2i - B*a*b*2i))/(2*a^3)))*(A*a^2*1i + A*b^2*2i - B*a*b*2i)*1i)/(a^3*d) - (b^2*atan(((b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4 + (b^2*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*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*b - B*a)*1i)/(a^5 - a^3*b^2) + (b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4 - (b^2*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*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*b - B*a)*1i)/(a^5 - a^3*b^2))/((16*(4*A^3*b^8 - 6*A^3*a*b^7 + 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 - 12*A^2*B*a*b^7 + 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))/a^6 + (b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4 + (b^2*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 - (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*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*b - B*a))/(a^5 - a^3*b^2) - (b^2*((a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 16*A^2*a*b^6 - 3*A^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 + 16*A*B*a*b^6 - 4*A*B*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))/a^4 - (b^2*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*A*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 - 2*A*a^9*b - 4*B*a^9*b))/a^6 + (8*b^2*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*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*b - B*a))/(a^5 - a^3*b^2)))*((a + b)*(a - b))^(1/2)*(A*b - B*a)*2i)/(d*(a^5 - a^3*b^2))","B"
318,1,4572,178,6.903551,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + b/cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^2+2\,A\,b^2+B\,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+A\,a\,b-2\,B\,a\,b\right)}{a^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^2-3\,B\,a\,b+3\,A\,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(A\,b-B\,a\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-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\right)}{a^6}-\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,1{}\mathrm{i}}{2\,a^4}\right)}{2\,a^4}+\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\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-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\right)}{a^6}+\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,1{}\mathrm{i}}{2\,a^4}\right)}{2\,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}-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+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\right)}{a^9}+\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\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-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\right)}{a^6}-\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,1{}\mathrm{i}}{2\,a^4}\right)\,1{}\mathrm{i}}{2\,a^4}-\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\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-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\right)}{a^6}+\frac{\left(a^2+2\,b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,4{}\mathrm{i}}{a^{10}}\right)\,1{}\mathrm{i}}{2\,a^4}\right)\,1{}\mathrm{i}}{2\,a^4}}\right)\,\left(a^2+2\,b^2\right)\,\left(A\,b-B\,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(A\,b-B\,a\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-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\right)}{a^6}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\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-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\right)}{a^6}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,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(A\,b-B\,a\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}+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}-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+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\right)}{a^9}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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-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\right)}{a^6}+\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\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-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\right)}{a^6}-\frac{b^3\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*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 + A*a*b - 2*B*a*b))/a^3 + (4*tan(c/2 + (d*x)/2)^3*(A*a^2 + 3*A*b^2 - 3*B*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)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - ((a^2 + 2*b^2)*(A*b - B*a)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*1i)/(2*a^4)))/(2*a^4) + ((a^2 + 2*b^2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + ((a^2 + 2*b^2)*(A*b - B*a)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*1i)/(2*a^4)))/(2*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 - 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))/a^9 + ((a^2 + 2*b^2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - ((a^2 + 2*b^2)*(A*b - B*a)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*1i)/(2*a^4))*1i)/(2*a^4) - ((a^2 + 2*b^2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + ((a^2 + 2*b^2)*(A*b - B*a)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*4i)/a^10)*1i)/(2*a^4))*1i)/(2*a^4)))*(a^2 + 2*b^2)*(A*b - B*a))/(a^4*d) - (b^3*atan(((b^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + (b^3*((a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - (b^3*((a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(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*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 - 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))/a^9 - (b^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + (b^3*((a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) + (b^3*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - (b^3*((a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (8*b^3*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*((a + b)*(a - b))^(1/2)*(A*b - B*a)*2i)/(d*(a^6 - a^4*b^2))","B"
319,1,5903,240,8.635606,"\text{Not used}","int((cos(c + d*x)^4*(A + B/cos(c + d*x)))/(a + b/cos(c + d*x)),x)","\frac{\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\,A\,a\,b^2-8\,A\,a^2\,b+8\,B\,a\,b^2-4\,B\,a^2\,b\right)}{4\,a^4}-\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\,A\,a\,b^2+8\,A\,a^2\,b-8\,B\,a\,b^2-4\,B\,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\,A\,a\,b^2+40\,A\,a^2\,b-72\,B\,a\,b^2+12\,B\,a^2\,b\right)}{12\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^3-72\,A\,b^3+40\,B\,a^3-12\,A\,a\,b^2-40\,A\,a^2\,b+72\,B\,a\,b^2+12\,B\,a^2\,b\right)}{12\,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}+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^2-12\,A\,a^{15}\,b-16\,B\,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(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{16\,a^{13}}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{8\,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\,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}+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\right)}{2\,a^8}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)\,1{}\mathrm{i}}{8\,a^5}-\frac{\left(\frac{\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,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(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{16\,a^{13}}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{8\,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\,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}+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\right)}{2\,a^8}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)\,1{}\mathrm{i}}{8\,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}-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}+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}}{a^{12}}+\frac{\left(\frac{\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,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(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{16\,a^{13}}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{8\,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\,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}+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\right)}{2\,a^8}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{8\,a^5}+\frac{\left(\frac{\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,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(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{16\,a^{13}}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{8\,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\,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}+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\right)}{2\,a^8}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)}{8\,a^5}}\right)\,\left(3{}\mathrm{i}\,A\,a^4-4{}\mathrm{i}\,B\,a^3\,b+4{}\mathrm{i}\,A\,a^2\,b^2-8{}\mathrm{i}\,B\,a\,b^3+8{}\mathrm{i}\,A\,b^4\right)\,1{}\mathrm{i}}{4\,a^5\,d}-\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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}+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\right)}{2\,a^8}+\frac{b^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b}{a^{12}}-\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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}+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\right)}{2\,a^8}-\frac{b^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b}{a^{12}}+\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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\,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}-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}+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}}{a^{12}}+\frac{b^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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}+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\right)}{2\,a^8}+\frac{b^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b}{a^{12}}-\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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}+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\right)}{2\,a^8}-\frac{b^4\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{12\,A\,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^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b}{a^{12}}+\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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(A\,b-B\,a\right)\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(5*A*a^3 - 8*A*b^3 + 8*B*a^3 + 4*A*a*b^2 - 8*A*a^2*b + 8*B*a*b^2 - 4*B*a^2*b))/(4*a^4) - (tan(c/2 + (d*x)/2)^7*(5*A*a^3 + 8*A*b^3 - 8*B*a^3 + 4*A*a*b^2 + 8*A*a^2*b - 8*B*a*b^2 - 4*B*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*A*a*b^2 + 40*A*a^2*b - 72*B*a*b^2 + 12*B*a^2*b))/(12*a^4) + (tan(c/2 + (d*x)/2)^5*(9*A*a^3 - 72*A*b^3 + 40*B*a^3 - 12*A*a*b^2 - 40*A*a^2*b + 72*B*a*b^2 + 12*B*a^2*b))/(12*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 + 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 - 12*A*a^15*b - 16*B*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*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(16*a^13))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(8*a^5) + (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i)*1i)/(8*a^5) - (((((12*A*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 - 12*A*a^15*b - 16*B*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*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(16*a^13))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(8*a^5) - (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i)*1i)/(8*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 - 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)/a^12 + (((((12*A*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 - 12*A*a^15*b - 16*B*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*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(16*a^13))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(8*a^5) + (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(8*a^5) + (((((12*A*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 - 12*A*a^15*b - 16*B*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*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(16*a^13))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(8*a^5) - (tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i))/(8*a^5)))*(A*a^4*3i + A*b^4*8i + A*a^2*b^2*4i - B*a*b^3*8i - B*a^3*b*4i)*1i)/(4*a^5*d) - (b^4*atan(((b^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8) + (b^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((12*A*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 - 12*A*a^15*b - 16*B*a^15*b)/a^12 - (b^4*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(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^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8) - (b^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((12*A*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 - 12*A*a^15*b - 16*B*a^15*b)/a^12 + (b^4*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(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*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 - 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)/a^12 + (b^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8) + (b^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((12*A*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 - 12*A*a^15*b - 16*B*a^15*b)/a^12 - (b^4*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(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^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 256*A^2*a*b^10 - 27*A^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 + 256*A*B*a*b^10 - 24*A*B*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))/(2*a^8) - (b^4*((a + b)*(a - b))^(1/2)*(A*b - B*a)*((12*A*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 - 12*A*a^15*b - 16*B*a^15*b)/a^12 + (b^4*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(A*b - B*a)*(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 - B*a)*2i)/(d*(a^7 - a^5*b^2))","B"
320,1,6678,272,11.171319,"\text{Not used}","int((A + B/cos(c + d*x))/(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(6\,B\,a^4-2\,A\,b^4+B\,b^4+2\,A\,a^2\,b^2-5\,B\,a^2\,b^2+2\,A\,a\,b^3-4\,A\,a^3\,b+3\,B\,a\,b^3-3\,B\,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\,B\,a^4+4\,A\,a^3\,b+3\,B\,a^2\,b^2-2\,A\,a\,b^3+B\,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\,A\,b^4+6\,B\,a^4+B\,b^4-2\,A\,a^2\,b^2-5\,B\,a^2\,b^2+2\,A\,a\,b^3-4\,A\,a^3\,b-3\,B\,a\,b^3+3\,B\,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\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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\,B\,a^2-4\,A\,a\,b+B\,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\,B\,a^2-4\,A\,a\,b+B\,b^2\right)}{2\,b^4}\right)\,\left(6\,B\,a^2-4\,A\,a\,b+B\,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\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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\,B\,a^2-4\,A\,a\,b+B\,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\,B\,a^2-4\,A\,a\,b+B\,b^2\right)}{2\,b^4}\right)\,\left(6\,B\,a^2-4\,A\,a\,b+B\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(-32\,A^3\,a^8\,b^3+16\,A^3\,a^7\,b^4+80\,A^3\,a^6\,b^5-24\,A^3\,a^5\,b^6-48\,A^3\,a^4\,b^7+144\,A^2\,B\,a^9\,b^2-72\,A^2\,B\,a^8\,b^3-336\,A^2\,B\,a^7\,b^4+108\,A^2\,B\,a^6\,b^5+168\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+24\,A^2\,B\,a^3\,b^8-216\,A\,B^2\,a^{10}\,b+108\,A\,B^2\,a^9\,b^2+468\,A\,B^2\,a^8\,b^3-162\,A\,B^2\,a^7\,b^4-186\,A\,B^2\,a^6\,b^5+15\,A\,B^2\,a^5\,b^6-63\,A\,B^2\,a^4\,b^7+3\,A\,B^2\,a^3\,b^8-3\,A\,B^2\,a^2\,b^9+108\,B^3\,a^{11}-54\,B^3\,a^{10}\,b-216\,B^3\,a^9\,b^2+81\,B^3\,a^8\,b^3+63\,B^3\,a^7\,b^4-9\,B^3\,a^6\,b^5+41\,B^3\,a^5\,b^6-4\,B^3\,a^4\,b^7+4\,B^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\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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\,B\,a^2-4\,A\,a\,b+B\,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\,B\,a^2-4\,A\,a\,b+B\,b^2\right)}{2\,b^4}\right)\,\left(6\,B\,a^2-4\,A\,a\,b+B\,b^2\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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\,B\,a^2-4\,A\,a\,b+B\,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\,B\,a^2-4\,A\,a\,b+B\,b^2\right)}{2\,b^4}\right)\,\left(6\,B\,a^2-4\,A\,a\,b+B\,b^2\right)}{2\,b^4}}\right)\,\left(6\,B\,a^2-4\,A\,a\,b+B\,b^2\right)\,1{}\mathrm{i}}{b^4\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,A^3\,a^8\,b^3+16\,A^3\,a^7\,b^4+80\,A^3\,a^6\,b^5-24\,A^3\,a^5\,b^6-48\,A^3\,a^4\,b^7+144\,A^2\,B\,a^9\,b^2-72\,A^2\,B\,a^8\,b^3-336\,A^2\,B\,a^7\,b^4+108\,A^2\,B\,a^6\,b^5+168\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+24\,A^2\,B\,a^3\,b^8-216\,A\,B^2\,a^{10}\,b+108\,A\,B^2\,a^9\,b^2+468\,A\,B^2\,a^8\,b^3-162\,A\,B^2\,a^7\,b^4-186\,A\,B^2\,a^6\,b^5+15\,A\,B^2\,a^5\,b^6-63\,A\,B^2\,a^4\,b^7+3\,A\,B^2\,a^3\,b^8-3\,A\,B^2\,a^2\,b^9+108\,B^3\,a^{11}-54\,B^3\,a^{10}\,b-216\,B^3\,a^9\,b^2+81\,B^3\,a^8\,b^3+63\,B^3\,a^7\,b^4-9\,B^3\,a^6\,b^5+41\,B^3\,a^5\,b^6-4\,B^3\,a^4\,b^7+4\,B^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{a^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}-\frac{a^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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,"(atan(-((((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(6*B*a^2 + B*b^2 - 4*A*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*B*a^2 + B*b^2 - 4*A*a*b))/(2*b^4))*(6*B*a^2 + B*b^2 - 4*A*a*b)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(6*B*a^2 + B*b^2 - 4*A*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*B*a^2 + B*b^2 - 4*A*a*b))/(2*b^4))*(6*B*a^2 + B*b^2 - 4*A*a*b)*1i)/(2*b^4))/((16*(108*B^3*a^11 - 54*B^3*a^10*b - 48*A^3*a^4*b^7 - 24*A^3*a^5*b^6 + 80*A^3*a^6*b^5 + 16*A^3*a^7*b^4 - 32*A^3*a^8*b^3 + 4*B^3*a^3*b^8 - 4*B^3*a^4*b^7 + 41*B^3*a^5*b^6 - 9*B^3*a^6*b^5 + 63*B^3*a^7*b^4 + 81*B^3*a^8*b^3 - 216*B^3*a^9*b^2 - 216*A*B^2*a^10*b - 3*A*B^2*a^2*b^9 + 3*A*B^2*a^3*b^8 - 63*A*B^2*a^4*b^7 + 15*A*B^2*a^5*b^6 - 186*A*B^2*a^6*b^5 - 162*A*B^2*a^7*b^4 + 468*A*B^2*a^8*b^3 + 108*A*B^2*a^9*b^2 + 24*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 168*A^2*B*a^5*b^6 + 108*A^2*B*a^6*b^5 - 336*A^2*B*a^7*b^4 - 72*A^2*B*a^8*b^3 + 144*A^2*B*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*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(6*B*a^2 + B*b^2 - 4*A*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*B*a^2 + B*b^2 - 4*A*a*b))/(2*b^4))*(6*B*a^2 + B*b^2 - 4*A*a*b))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(6*B*a^2 + B*b^2 - 4*A*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*B*a^2 + B*b^2 - 4*A*a*b))/(2*b^4))*(6*B*a^2 + B*b^2 - 4*A*a*b))/(2*b^4)))*(6*B*a^2 + B*b^2 - 4*A*a*b)*1i)/(b^4*d) - ((tan(c/2 + (d*x)/2)^5*(6*B*a^4 - 2*A*b^4 + B*b^4 + 2*A*a^2*b^2 - 5*B*a^2*b^2 + 2*A*a*b^3 - 4*A*a^3*b + 3*B*a*b^3 - 3*B*a^3*b))/((a*b^3 - b^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(B*b^4 - 6*B*a^4 + 3*B*a^2*b^2 - 2*A*a*b^3 + 4*A*a^3*b))/(b*(a*b^2 - b^3)*(a + b)) + (tan(c/2 + (d*x)/2)*(2*A*b^4 + 6*B*a^4 + B*b^4 - 2*A*a^2*b^2 - 5*B*a^2*b^2 + 2*A*a*b^3 - 4*A*a^3*b - 3*B*a*b^3 + 3*B*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^2*atan(((a^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*B^3*a^11 - 54*B^3*a^10*b - 48*A^3*a^4*b^7 - 24*A^3*a^5*b^6 + 80*A^3*a^6*b^5 + 16*A^3*a^7*b^4 - 32*A^3*a^8*b^3 + 4*B^3*a^3*b^8 - 4*B^3*a^4*b^7 + 41*B^3*a^5*b^6 - 9*B^3*a^6*b^5 + 63*B^3*a^7*b^4 + 81*B^3*a^8*b^3 - 216*B^3*a^9*b^2 - 216*A*B^2*a^10*b - 3*A*B^2*a^2*b^9 + 3*A*B^2*a^3*b^8 - 63*A*B^2*a^4*b^7 + 15*A*B^2*a^5*b^6 - 186*A*B^2*a^6*b^5 - 162*A*B^2*a^7*b^4 + 468*A*B^2*a^8*b^3 + 108*A*B^2*a^9*b^2 + 24*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 168*A^2*B*a^5*b^6 + 108*A^2*B*a^6*b^5 - 336*A^2*B*a^7*b^4 - 72*A^2*B*a^8*b^3 + 144*A^2*B*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (a^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) - (a^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
321,1,5436,164,10.257307,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^3*(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^2\,b-B\,b^3-2\,B\,a^3+B\,a\,b^2+B\,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(B\,b^3-2\,B\,a^3+A\,a^2\,b+B\,a\,b^2-B\,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(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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(A\,b-2\,B\,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(A\,b-2\,B\,a\right)}{b^3}\right)\,\left(A\,b-2\,B\,a\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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(A\,b-2\,B\,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(A\,b-2\,B\,a\right)}{b^3}\right)\,\left(A\,b-2\,B\,a\right)\,1{}\mathrm{i}}{b^3}}{\frac{64\,\left(-A^3\,a^5\,b^3+A^3\,a^4\,b^4+3\,A^3\,a^3\,b^5-2\,A^3\,a^2\,b^6-2\,A^3\,a\,b^7+6\,A^2\,B\,a^6\,b^2-5\,A^2\,B\,a^5\,b^3-17\,A^2\,B\,a^4\,b^4+9\,A^2\,B\,a^3\,b^5+11\,A^2\,B\,a^2\,b^6-12\,A\,B^2\,a^7\,b+8\,A\,B^2\,a^6\,b^2+32\,A\,B^2\,a^5\,b^3-13\,A\,B^2\,a^4\,b^4-20\,A\,B^2\,a^3\,b^5+8\,B^3\,a^8-4\,B^3\,a^7\,b-20\,B^3\,a^6\,b^2+6\,B^3\,a^5\,b^3+12\,B^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(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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(A\,b-2\,B\,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(A\,b-2\,B\,a\right)}{b^3}\right)\,\left(A\,b-2\,B\,a\right)}{b^3}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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(A\,b-2\,B\,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(A\,b-2\,B\,a\right)}{b^3}\right)\,\left(A\,b-2\,B\,a\right)}{b^3}}\right)\,\left(A\,b-2\,B\,a\right)\,2{}\mathrm{i}}{b^3\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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(-A^3\,a^5\,b^3+A^3\,a^4\,b^4+3\,A^3\,a^3\,b^5-2\,A^3\,a^2\,b^6-2\,A^3\,a\,b^7+6\,A^2\,B\,a^6\,b^2-5\,A^2\,B\,a^5\,b^3-17\,A^2\,B\,a^4\,b^4+9\,A^2\,B\,a^3\,b^5+11\,A^2\,B\,a^2\,b^6-12\,A\,B^2\,a^7\,b+8\,A\,B^2\,a^6\,b^2+32\,A\,B^2\,a^5\,b^3-13\,A\,B^2\,a^4\,b^4-20\,A\,B^2\,a^3\,b^5+8\,B^3\,a^8-4\,B^3\,a^7\,b-20\,B^3\,a^6\,b^2+6\,B^3\,a^5\,b^3+12\,B^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}-\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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*(A*a^2*b - B*b^3 - 2*B*a^3 + B*a*b^2 + B*a^2*b))/(b^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)*(B*b^3 - 2*B*a^3 + A*a^2*b + B*a*b^2 - B*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*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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 - 2*B*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)))*(A*b - 2*B*a))/b^3)*(A*b - 2*B*a)*1i)/b^3 + (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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 - 2*B*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)))*(A*b - 2*B*a))/b^3)*(A*b - 2*B*a)*1i)/b^3)/((64*(8*B^3*a^8 - 2*A^3*a*b^7 - 4*B^3*a^7*b - 2*A^3*a^2*b^6 + 3*A^3*a^3*b^5 + A^3*a^4*b^4 - A^3*a^5*b^3 + 12*B^3*a^4*b^4 + 6*B^3*a^5*b^3 - 20*B^3*a^6*b^2 - 12*A*B^2*a^7*b - 20*A*B^2*a^3*b^5 - 13*A*B^2*a^4*b^4 + 32*A*B^2*a^5*b^3 + 8*A*B^2*a^6*b^2 + 11*A^2*B*a^2*b^6 + 9*A^2*B*a^3*b^5 - 17*A^2*B*a^4*b^4 - 5*A^2*B*a^5*b^3 + 6*A^2*B*a^6*b^2))/(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*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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 - 2*B*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)))*(A*b - 2*B*a))/b^3)*(A*b - 2*B*a))/b^3 - (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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 - 2*B*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)))*(A*b - 2*B*a))/b^3)*(A*b - 2*B*a))/b^3))*(A*b - 2*B*a)*2i)/(b^3*d) + (a*atan(((a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*B^3*a^8 - 2*A^3*a*b^7 - 4*B^3*a^7*b - 2*A^3*a^2*b^6 + 3*A^3*a^3*b^5 + A^3*a^4*b^4 - A^3*a^5*b^3 + 12*B^3*a^4*b^4 + 6*B^3*a^5*b^3 - 20*B^3*a^6*b^2 - 12*A*B^2*a^7*b - 20*A*B^2*a^3*b^5 - 13*A*B^2*a^4*b^4 + 32*A*B^2*a^5*b^3 + 8*A*B^2*a^6*b^2 + 11*A^2*B*a^2*b^6 + 9*A^2*B*a^3*b^5 - 17*A^2*B*a^4*b^4 - 5*A^2*B*a^5*b^3 + 6*A^2*B*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) - (a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
322,1,3751,131,9.653825,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^2*(a + b/cos(c + d*x))^2),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a^2-A\,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{B\,\mathrm{atan}\left(\frac{\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,B\,\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\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)\,1{}\mathrm{i}}{b^2}-\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,B\,\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\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}\right)\,1{}\mathrm{i}}{b^2}}{\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,B\,\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\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^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\,B\,b^5+A\,B^2\,a^3\,b^2+A\,B^2\,a^2\,b^3-3\,A\,B^2\,a\,b^4-A\,B^2\,b^5+B^3\,a^5-B^3\,a^4\,b-3\,B^3\,a^3\,b^2+2\,B^3\,a^2\,b^3+2\,B^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,B\,\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\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^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(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(A^2\,B\,b^5+A\,B^2\,a^3\,b^2+A\,B^2\,a^2\,b^3-3\,A\,B^2\,a\,b^4-A\,B^2\,b^5+B^3\,a^5-B^3\,a^4\,b-3\,B^3\,a^3\,b^2+2\,B^3\,a^2\,b^3+2\,B^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\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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,"- (B*atan(((B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 - (B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2)/((B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2 - (64*(B^3*a^5 - A*B^2*b^5 + A^2*B*b^5 + 2*B^3*a*b^4 - B^3*a^4*b + 2*B^3*a^2*b^3 - 3*B^3*a^3*b^2 - 3*A*B^2*a*b^4 + A*B^2*a^2*b^3 + A*B^2*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(B^3*a^5 - A*B^2*b^5 + A^2*B*b^5 + 2*B^3*a*b^4 - B^3*a^4*b + 2*B^3*a^2*b^3 - 3*B^3*a^3*b^2 - 3*A*B^2*a*b^4 + A*B^2*a^2*b^3 + A*B^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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(B*a^2 - A*a*b))/(d*(a + b)*(a*b - b^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
323,1,106,100,2.422386,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(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(A\,a-B\,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(A\,b-B\,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))*(A*a - B*b))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (2*tan(c/2 + (d*x)/2)*(A*b - B*a))/(d*(a + b)*(a - b)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
324,1,3763,124,9.655601,"\text{Not used}","int((A + B/cos(c + d*x))/(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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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\,B^2\,a^5\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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(A\,b^2-B\,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{\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\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\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\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,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\,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\,B^2\,a^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\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\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\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\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,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*A*atan(((A*((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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2 - (A*((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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^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*B*a^2*b^3 + A^2*B*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 - 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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 + (A*((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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)))/(a^2*d) + (atan(((((a + b)^3*(a - b)^3)^(1/2)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((a + b)^3*(a - b)^3)^(1/2)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*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*B*a^2*b^3 + A^2*B*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (((a + b)^3*(a - b)^3)^(1/2)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*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)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*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)*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 - B*a*b))/(d*(a + b)*(a*b - a^2)*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
325,1,3264,180,7.073498,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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\,b^2-2\,A\,b^3-A\,a^3+A\,a^2\,b+B\,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(A\,a^3-2\,A\,b^3-A\,a\,b^2+A\,a^2\,b+B\,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\,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{b\,\mathrm{atan}\left(\frac{\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,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+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^6-2\,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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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*(A*a*b^2 - 2*A*b^3 - A*a^3 + A*a^2*b + B*a*b^2))/(a^2*(a + b)*(a - b)) + (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))/(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) - (b*atan(((b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*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 - 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 + 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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*b^2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
326,1,6731,261,11.106278,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(a + b/cos(c + d*x))^2,x)","-\frac{\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^2-3\,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)\,\left(A\,a^4+6\,A\,b^4+2\,B\,a^4-5\,A\,a^2\,b^2-2\,B\,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^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+4\,B\,a\,b^3-6\,A\,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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\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(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\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(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}+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^9-48\,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\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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\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(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{2\,a^4}+\frac{\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\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(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{2\,a^4}\right)\,\left(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)}{2\,a^4}}\right)\,\left(1{}\mathrm{i}\,A\,a^2-4{}\mathrm{i}\,B\,a\,b+6{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^4\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,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}+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^9-48\,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\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{b^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,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,"(b^2*atan(((b^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((8*(2*A*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 - 8*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^2*((8*(2*A*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 - 8*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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 - 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 - 216*A^2*B*a*b^10 + 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))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (b^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((8*(2*A*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 - 8*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^2*((a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^2*((8*(2*A*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 - 8*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*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*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)) - (atan(-((((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*6i - B*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)))*(A*a^2*1i + A*b^2*6i - B*a*b*4i))/(2*a^4))*(A*a^2*1i + A*b^2*6i - B*a*b*4i)*1i)/(2*a^4) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*6i - B*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)))*(A*a^2*1i + A*b^2*6i - B*a*b*4i))/(2*a^4))*(A*a^2*1i + A*b^2*6i - B*a*b*4i)*1i)/(2*a^4))/((16*(108*A^3*b^11 - 54*A^3*a*b^10 - 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 - 216*A^2*B*a*b^10 + 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))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*6i - B*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)))*(A*a^2*1i + A*b^2*6i - B*a*b*4i))/(2*a^4))*(A*a^2*1i + A*b^2*6i - B*a*b*4i))/(2*a^4) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*6i - B*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)))*(A*a^2*1i + A*b^2*6i - B*a*b*4i))/(2*a^4))*(A*a^2*1i + A*b^2*6i - B*a*b*4i))/(2*a^4)))*(A*a^2*1i + A*b^2*6i - B*a*b*4i)*1i)/(a^4*d) - ((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 - 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)*(A*a^4 + 6*A*b^4 + 2*B*a^4 - 5*A*a^2*b^2 - 2*B*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 + 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"
327,1,7763,346,11.663047,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^5+8\,A\,b^5-B\,a^5-6\,A\,a^2\,b^3+2\,A\,a^3\,b^2+3\,B\,a^2\,b^3+5\,B\,a^3\,b^2-4\,A\,a\,b^4-6\,B\,a\,b^4-3\,B\,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)\,\left(2\,A\,a^5-8\,A\,b^5+B\,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\,A\,a\,b^4+6\,B\,a\,b^4-3\,B\,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^5-38\,A\,a^2\,b^3-14\,A\,a^3\,b^2-9\,B\,a^2\,b^3+33\,B\,a^3\,b^2+12\,A\,a\,b^4-16\,A\,a^4\,b-54\,B\,a\,b^4+9\,B\,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+38\,A\,a^2\,b^3-14\,A\,a^3\,b^2-9\,B\,a^2\,b^3-33\,B\,a^3\,b^2+12\,A\,a\,b^4+16\,A\,a^4\,b+54\,B\,a\,b^4+9\,B\,a^4\,b\right)}{3\,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^2-4\,A\,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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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^2-4\,A\,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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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}+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}-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}\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^2-4\,A\,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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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^2-4\,A\,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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\right)}{a^5}}\right)\,\left(-\frac{1{}\mathrm{i}\,B\,a^3}{2}+1{}\mathrm{i}\,A\,a^2\,b-3{}\mathrm{i}\,B\,a\,b^2+4{}\mathrm{i}\,A\,b^3\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^3\,\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^2-4\,A\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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)}{\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\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^3\,\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^2-4\,A\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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)}{\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\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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}+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}-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}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^3\,\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^2-4\,A\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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)}{\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\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}-\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}+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}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^3\,\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^2-4\,A\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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)}{\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\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\left(4\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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\,B\,a^3-5\,A\,a^2\,b-3\,B\,a\,b^2+4\,A\,b^3\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)^7*(2*A*a^5 + 8*A*b^5 - B*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*A*a*b^4 - 6*B*a*b^4 - 3*B*a^4*b))/(a^4*(a + b)*(a - b)) - (tan(c/2 + (d*x)/2)*(2*A*a^5 - 8*A*b^5 + B*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*A*a*b^4 + 6*B*a*b^4 - 3*B*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 - 38*A*a^2*b^3 - 14*A*a^3*b^2 - 9*B*a^2*b^3 + 33*B*a^3*b^2 + 12*A*a*b^4 - 16*A*a^4*b - 54*B*a*b^4 + 9*B*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 + 38*A*a^2*b^3 - 14*A*a^3*b^2 - 9*B*a^2*b^3 - 33*B*a^3*b^2 + 12*A*a*b^4 + 16*A*a^4*b + 54*B*a*b^4 + 9*B*a^4*b))/(3*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 - 4*A*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*a^2*b*1i - 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*a^2*b*1i - 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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + A*a^2*b*1i - 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 - 4*A*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*a^2*b*1i - 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*a^2*b*1i - 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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + A*a^2*b*1i - 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 - 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))/(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 - 4*A*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*a^2*b*1i - 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*a^2*b*1i - 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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + A*a^2*b*1i - 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 - 4*A*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*a^2*b*1i - 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*a^2*b*1i - 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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(A*b^3*4i - (B*a^3*1i)/2 + A*a^2*b*1i - B*a*b^2*3i))/a^5))*(A*b^3*4i - (B*a^3*1i)/2 + A*a^2*b*1i - B*a*b^2*3i)*2i)/(a^5*d) - (b^3*atan(((b^3*((a + b)^3*(a - b)^3)^(1/2)*((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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^3*((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 - 4*A*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*b^3*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^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))/((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^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^3*((a + b)^3*(a - b)^3)^(1/2)*((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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^3*((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 - 4*A*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*b^3*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^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))/((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^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2)*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 - 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))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b^3*((a + b)^3*(a - b)^3)^(1/2)*((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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^3*((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 - 4*A*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*b^3*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^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))/((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^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) - (b^3*((a + b)^3*(a - b)^3)^(1/2)*((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 - 192*A*B*a*b^11 - 4*A*B*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))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^3*((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 - 4*A*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*b^3*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^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))/((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^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(4*A*b^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*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^3 + 4*B*a^3 - 5*A*a^2*b - 3*B*a*b^2)*2i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
328,1,10533,407,14.229301,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^5*(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^7+36\,B\,a^7+3\,B\,b^7-10\,A\,a^2\,b^5+16\,A\,a^3\,b^4+35\,A\,a^4\,b^3-9\,A\,a^5\,b^2+5\,B\,a^2\,b^5+26\,B\,a^3\,b^4-29\,B\,a^4\,b^3-67\,B\,a^5\,b^2-4\,A\,a\,b^6-18\,A\,a^6\,b-4\,B\,a\,b^6+18\,B\,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\,B\,b^7-36\,B\,a^7-2\,A\,b^7+10\,A\,a^2\,b^5+16\,A\,a^3\,b^4-35\,A\,a^4\,b^3-9\,A\,a^5\,b^2+5\,B\,a^2\,b^5-26\,B\,a^3\,b^4-29\,B\,a^4\,b^3+67\,B\,a^5\,b^2-4\,A\,a\,b^6+18\,A\,a^6\,b+4\,B\,a\,b^6+18\,B\,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(B\,b^6-12\,B\,a^6-2\,A\,b^6+4\,A\,a^2\,b^4-12\,A\,a^3\,b^3-3\,A\,a^4\,b^2-8\,B\,a^2\,b^4-10\,B\,a^3\,b^3+23\,B\,a^4\,b^2+2\,A\,a\,b^5+6\,A\,a^5\,b+5\,B\,a\,b^5+6\,B\,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\,A\,b^6-12\,B\,a^6+B\,b^6-4\,A\,a^2\,b^4-12\,A\,a^3\,b^3+3\,A\,a^4\,b^2-8\,B\,a^2\,b^4+10\,B\,a^3\,b^3+23\,B\,a^4\,b^2+2\,A\,a\,b^5+6\,A\,a^5\,b-5\,B\,a\,b^5-6\,B\,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{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,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(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)}{2\,b^5}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)\,1{}\mathrm{i}}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,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(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)}{2\,b^5}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(-216\,A^3\,a^{12}\,b^3+108\,A^3\,a^{11}\,b^4+972\,A^3\,a^{10}\,b^5-486\,A^3\,a^9\,b^6-1728\,A^3\,a^8\,b^7+756\,A^3\,a^7\,b^8+1404\,A^3\,a^6\,b^9-432\,A^3\,a^5\,b^{10}-432\,A^3\,a^4\,b^{11}+1296\,A^2\,B\,a^{13}\,b^2-648\,A^2\,B\,a^{12}\,b^3-5724\,A^2\,B\,a^{11}\,b^4+2808\,A^2\,B\,a^{10}\,b^5+9828\,A^2\,B\,a^9\,b^6-4203\,A^2\,B\,a^8\,b^7-7524\,A^2\,B\,a^7\,b^8+2268\,A^2\,B\,a^6\,b^9+1980\,A^2\,B\,a^5\,b^{10}+144\,A^2\,B\,a^3\,b^{12}-2592\,A\,B^2\,a^{14}\,b+1296\,A\,B^2\,a^{13}\,b^2+11232\,A\,B^2\,a^{12}\,b^3-5400\,A\,B^2\,a^{11}\,b^4-18594\,A\,B^2\,a^{10}\,b^5+7767\,A\,B^2\,a^9\,b^6+13347\,A\,B^2\,a^8\,b^7-3972\,A\,B^2\,a^7\,b^8-2892\,A\,B^2\,a^6\,b^9+9\,A\,B^2\,a^5\,b^{10}-489\,A\,B^2\,a^4\,b^{11}+12\,A\,B^2\,a^3\,b^{12}-12\,A\,B^2\,a^2\,b^{13}+1728\,B^3\,a^{15}-864\,B^3\,a^{14}\,b-7344\,B^3\,a^{13}\,b^2+3456\,B^3\,a^{12}\,b^3+11700\,B^3\,a^{11}\,b^4-4770\,B^3\,a^{10}\,b^5-7829\,B^3\,a^9\,b^6+2326\,B^3\,a^8\,b^7+1314\,B^3\,a^7\,b^8-11\,B^3\,a^6\,b^9+411\,B^3\,a^5\,b^{10}-20\,B^3\,a^4\,b^{11}+20\,B^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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,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(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)}{2\,b^5}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,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(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)}{2\,b^5}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)}{2\,b^5}}\right)\,\left(12\,B\,a^2-6\,A\,a\,b+B\,b^2\right)\,1{}\mathrm{i}}{b^5\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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^2\,\left(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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^2\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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^2\,\left(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-216\,A^3\,a^{12}\,b^3+108\,A^3\,a^{11}\,b^4+972\,A^3\,a^{10}\,b^5-486\,A^3\,a^9\,b^6-1728\,A^3\,a^8\,b^7+756\,A^3\,a^7\,b^8+1404\,A^3\,a^6\,b^9-432\,A^3\,a^5\,b^{10}-432\,A^3\,a^4\,b^{11}+1296\,A^2\,B\,a^{13}\,b^2-648\,A^2\,B\,a^{12}\,b^3-5724\,A^2\,B\,a^{11}\,b^4+2808\,A^2\,B\,a^{10}\,b^5+9828\,A^2\,B\,a^9\,b^6-4203\,A^2\,B\,a^8\,b^7-7524\,A^2\,B\,a^7\,b^8+2268\,A^2\,B\,a^6\,b^9+1980\,A^2\,B\,a^5\,b^{10}+144\,A^2\,B\,a^3\,b^{12}-2592\,A\,B^2\,a^{14}\,b+1296\,A\,B^2\,a^{13}\,b^2+11232\,A\,B^2\,a^{12}\,b^3-5400\,A\,B^2\,a^{11}\,b^4-18594\,A\,B^2\,a^{10}\,b^5+7767\,A\,B^2\,a^9\,b^6+13347\,A\,B^2\,a^8\,b^7-3972\,A\,B^2\,a^7\,b^8-2892\,A\,B^2\,a^6\,b^9+9\,A\,B^2\,a^5\,b^{10}-489\,A\,B^2\,a^4\,b^{11}+12\,A\,B^2\,a^3\,b^{12}-12\,A\,B^2\,a^2\,b^{13}+1728\,B^3\,a^{15}-864\,B^3\,a^{14}\,b-7344\,B^3\,a^{13}\,b^2+3456\,B^3\,a^{12}\,b^3+11700\,B^3\,a^{11}\,b^4-4770\,B^3\,a^{10}\,b^5-7829\,B^3\,a^9\,b^6+2326\,B^3\,a^8\,b^7+1314\,B^3\,a^7\,b^8-11\,B^3\,a^6\,b^9+411\,B^3\,a^5\,b^{10}-20\,B^3\,a^4\,b^{11}+20\,B^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^2\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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^2\,\left(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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^2\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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^2\,\left(\frac{4\,\left(4\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,b^5\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*A*b^7 + 36*B*a^7 + 3*B*b^7 - 10*A*a^2*b^5 + 16*A*a^3*b^4 + 35*A*a^4*b^3 - 9*A*a^5*b^2 + 5*B*a^2*b^5 + 26*B*a^3*b^4 - 29*B*a^4*b^3 - 67*B*a^5*b^2 - 4*A*a*b^6 - 18*A*a^6*b - 4*B*a*b^6 + 18*B*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^5*(3*B*b^7 - 36*B*a^7 - 2*A*b^7 + 10*A*a^2*b^5 + 16*A*a^3*b^4 - 35*A*a^4*b^3 - 9*A*a^5*b^2 + 5*B*a^2*b^5 - 26*B*a^3*b^4 - 29*B*a^4*b^3 + 67*B*a^5*b^2 - 4*A*a*b^6 + 18*A*a^6*b + 4*B*a*b^6 + 18*B*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^7*(B*b^6 - 12*B*a^6 - 2*A*b^6 + 4*A*a^2*b^4 - 12*A*a^3*b^3 - 3*A*a^4*b^2 - 8*B*a^2*b^4 - 10*B*a^3*b^3 + 23*B*a^4*b^2 + 2*A*a*b^5 + 6*A*a^5*b + 5*B*a*b^5 + 6*B*a^5*b))/((a*b^4 - b^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^6 - 12*B*a^6 + B*b^6 - 4*A*a^2*b^4 - 12*A*a^3*b^3 + 3*A*a^4*b^2 - 8*B*a^2*b^4 + 10*B*a^3*b^3 + 23*B*a^4*b^2 + 2*A*a*b^5 + 6*A*a^5*b - 5*B*a*b^5 - 6*B*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(((((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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) - (((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(12*B*a^2 + B*b^2 - 6*A*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)))*(12*B*a^2 + B*b^2 - 6*A*a*b))/(2*b^5))*(12*B*a^2 + B*b^2 - 6*A*a*b)*1i)/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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) + (((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(12*B*a^2 + B*b^2 - 6*A*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)))*(12*B*a^2 + B*b^2 - 6*A*a*b))/(2*b^5))*(12*B*a^2 + B*b^2 - 6*A*a*b)*1i)/(2*b^5))/((8*(1728*B^3*a^15 - 864*B^3*a^14*b - 432*A^3*a^4*b^11 - 432*A^3*a^5*b^10 + 1404*A^3*a^6*b^9 + 756*A^3*a^7*b^8 - 1728*A^3*a^8*b^7 - 486*A^3*a^9*b^6 + 972*A^3*a^10*b^5 + 108*A^3*a^11*b^4 - 216*A^3*a^12*b^3 + 20*B^3*a^3*b^12 - 20*B^3*a^4*b^11 + 411*B^3*a^5*b^10 - 11*B^3*a^6*b^9 + 1314*B^3*a^7*b^8 + 2326*B^3*a^8*b^7 - 7829*B^3*a^9*b^6 - 4770*B^3*a^10*b^5 + 11700*B^3*a^11*b^4 + 3456*B^3*a^12*b^3 - 7344*B^3*a^13*b^2 - 2592*A*B^2*a^14*b - 12*A*B^2*a^2*b^13 + 12*A*B^2*a^3*b^12 - 489*A*B^2*a^4*b^11 + 9*A*B^2*a^5*b^10 - 2892*A*B^2*a^6*b^9 - 3972*A*B^2*a^7*b^8 + 13347*A*B^2*a^8*b^7 + 7767*A*B^2*a^9*b^6 - 18594*A*B^2*a^10*b^5 - 5400*A*B^2*a^11*b^4 + 11232*A*B^2*a^12*b^3 + 1296*A*B^2*a^13*b^2 + 144*A^2*B*a^3*b^12 + 1980*A^2*B*a^5*b^10 + 2268*A^2*B*a^6*b^9 - 7524*A^2*B*a^7*b^8 - 4203*A^2*B*a^8*b^7 + 9828*A^2*B*a^9*b^6 + 2808*A^2*B*a^10*b^5 - 5724*A^2*B*a^11*b^4 - 648*A^2*B*a^12*b^3 + 1296*A^2*B*a^13*b^2))/(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)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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) - (((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(12*B*a^2 + B*b^2 - 6*A*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)))*(12*B*a^2 + B*b^2 - 6*A*a*b))/(2*b^5))*(12*B*a^2 + B*b^2 - 6*A*a*b))/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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) + (((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(12*B*a^2 + B*b^2 - 6*A*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)))*(12*B*a^2 + B*b^2 - 6*A*a*b))/(2*b^5))*(12*B*a^2 + B*b^2 - 6*A*a*b))/(2*b^5)))*(12*B*a^2 + B*b^2 - 6*A*a*b)*1i)/(b^5*d) - (a^2*atan(((a^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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^2*((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*(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)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*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^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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^2*((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*(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)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*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*B^3*a^15 - 864*B^3*a^14*b - 432*A^3*a^4*b^11 - 432*A^3*a^5*b^10 + 1404*A^3*a^6*b^9 + 756*A^3*a^7*b^8 - 1728*A^3*a^8*b^7 - 486*A^3*a^9*b^6 + 972*A^3*a^10*b^5 + 108*A^3*a^11*b^4 - 216*A^3*a^12*b^3 + 20*B^3*a^3*b^12 - 20*B^3*a^4*b^11 + 411*B^3*a^5*b^10 - 11*B^3*a^6*b^9 + 1314*B^3*a^7*b^8 + 2326*B^3*a^8*b^7 - 7829*B^3*a^9*b^6 - 4770*B^3*a^10*b^5 + 11700*B^3*a^11*b^4 + 3456*B^3*a^12*b^3 - 7344*B^3*a^13*b^2 - 2592*A*B^2*a^14*b - 12*A*B^2*a^2*b^13 + 12*A*B^2*a^3*b^12 - 489*A*B^2*a^4*b^11 + 9*A*B^2*a^5*b^10 - 2892*A*B^2*a^6*b^9 - 3972*A*B^2*a^7*b^8 + 13347*A*B^2*a^8*b^7 + 7767*A*B^2*a^9*b^6 - 18594*A*B^2*a^10*b^5 - 5400*A*B^2*a^11*b^4 + 11232*A*B^2*a^12*b^3 + 1296*A*B^2*a^13*b^2 + 144*A^2*B*a^3*b^12 + 1980*A^2*B*a^5*b^10 + 2268*A^2*B*a^6*b^9 - 7524*A^2*B*a^7*b^8 - 4203*A^2*B*a^8*b^7 + 9828*A^2*B*a^9*b^6 + 2808*A^2*B*a^10*b^5 - 5724*A^2*B*a^11*b^4 - 648*A^2*B*a^12*b^3 + 1296*A^2*B*a^13*b^2))/(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^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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^2*((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*(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)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4))/(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^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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^2*((4*(4*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*(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)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4))/(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)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*a*b^4)*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"
329,1,9286,289,14.543179,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}^5\,\left(6\,B\,a^5-2\,B\,b^5+6\,A\,a^2\,b^3+A\,a^3\,b^2+4\,B\,a^2\,b^3-12\,B\,a^3\,b^2-2\,A\,a^4\,b+2\,B\,a\,b^4-3\,B\,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\,B\,a^5+2\,B\,b^5+6\,A\,a^2\,b^3-A\,a^3\,b^2-4\,B\,a^2\,b^3-12\,B\,a^3\,b^2-2\,A\,a^4\,b+2\,B\,a\,b^4+3\,B\,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\,B\,a^6-2\,A\,a^5\,b-13\,B\,a^4\,b^2+5\,A\,a^3\,b^3+6\,B\,a^2\,b^4-2\,B\,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(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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(A\,b-3\,B\,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(A\,b-3\,B\,a\right)}{b^4}\right)\,\left(A\,b-3\,B\,a\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^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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(A\,b-3\,B\,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(A\,b-3\,B\,a\right)}{b^4}\right)\,\left(A\,b-3\,B\,a\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(-4\,A^3\,a^9\,b^3+2\,A^3\,a^8\,b^4+18\,A^3\,a^7\,b^5-13\,A^3\,a^6\,b^6-36\,A^3\,a^5\,b^7+26\,A^3\,a^4\,b^8+34\,A^3\,a^3\,b^9-24\,A^3\,a^2\,b^{10}-12\,A^3\,a\,b^{11}+36\,A^2\,B\,a^{10}\,b^2-18\,A^2\,B\,a^9\,b^3-162\,A^2\,B\,a^8\,b^4+105\,A^2\,B\,a^7\,b^5+312\,A^2\,B\,a^6\,b^6-198\,A^2\,B\,a^5\,b^7-282\,A^2\,B\,a^4\,b^8+156\,A^2\,B\,a^3\,b^9+96\,A^2\,B\,a^2\,b^{10}-108\,A\,B^2\,a^{11}\,b+54\,A\,B^2\,a^{10}\,b^2+486\,A\,B^2\,a^9\,b^3-279\,A\,B^2\,a^8\,b^4-900\,A\,B^2\,a^7\,b^5+486\,A\,B^2\,a^6\,b^6+774\,A\,B^2\,a^5\,b^7-324\,A\,B^2\,a^4\,b^8-252\,A\,B^2\,a^3\,b^9+108\,B^3\,a^{12}-54\,B^3\,a^{11}\,b-486\,B^3\,a^{10}\,b^2+243\,B^3\,a^9\,b^3+864\,B^3\,a^8\,b^4-378\,B^3\,a^7\,b^5-702\,B^3\,a^6\,b^6+216\,B^3\,a^5\,b^7+216\,B^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(8\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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(A\,b-3\,B\,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(A\,b-3\,B\,a\right)}{b^4}\right)\,\left(A\,b-3\,B\,a\right)}{b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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(A\,b-3\,B\,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(A\,b-3\,B\,a\right)}{b^4}\right)\,\left(A\,b-3\,B\,a\right)}{b^4}}\right)\,\left(A\,b-3\,B\,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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,A^3\,a^9\,b^3+2\,A^3\,a^8\,b^4+18\,A^3\,a^7\,b^5-13\,A^3\,a^6\,b^6-36\,A^3\,a^5\,b^7+26\,A^3\,a^4\,b^8+34\,A^3\,a^3\,b^9-24\,A^3\,a^2\,b^{10}-12\,A^3\,a\,b^{11}+36\,A^2\,B\,a^{10}\,b^2-18\,A^2\,B\,a^9\,b^3-162\,A^2\,B\,a^8\,b^4+105\,A^2\,B\,a^7\,b^5+312\,A^2\,B\,a^6\,b^6-198\,A^2\,B\,a^5\,b^7-282\,A^2\,B\,a^4\,b^8+156\,A^2\,B\,a^3\,b^9+96\,A^2\,B\,a^2\,b^{10}-108\,A\,B^2\,a^{11}\,b+54\,A\,B^2\,a^{10}\,b^2+486\,A\,B^2\,a^9\,b^3-279\,A\,B^2\,a^8\,b^4-900\,A\,B^2\,a^7\,b^5+486\,A\,B^2\,a^6\,b^6+774\,A\,B^2\,a^5\,b^7-324\,A\,B^2\,a^4\,b^8-252\,A\,B^2\,a^3\,b^9+108\,B^3\,a^{12}-54\,B^3\,a^{11}\,b-486\,B^3\,a^{10}\,b^2+243\,B^3\,a^9\,b^3+864\,B^3\,a^8\,b^4-378\,B^3\,a^7\,b^5-702\,B^3\,a^6\,b^6+216\,B^3\,a^5\,b^7+216\,B^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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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*B*a^5 - 2*B*b^5 + 6*A*a^2*b^3 + A*a^3*b^2 + 4*B*a^2*b^3 - 12*B*a^3*b^2 - 2*A*a^4*b + 2*B*a*b^4 - 3*B*a^4*b))/((a*b^3 - b^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(6*B*a^5 + 2*B*b^5 + 6*A*a^2*b^3 - A*a^3*b^2 - 4*B*a^2*b^3 - 12*B*a^3*b^2 - 2*A*a^4*b + 2*B*a*b^4 + 3*B*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) - (2*tan(c/2 + (d*x)/2)^3*(6*B*a^6 - 2*B*b^6 + 5*A*a^3*b^3 + 6*B*a^2*b^4 - 13*B*a^4*b^2 - 2*A*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(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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)*(A*b - 3*B*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)))*(A*b - 3*B*a))/b^4)*(A*b - 3*B*a)*1i)/b^4 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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)*(A*b - 3*B*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)))*(A*b - 3*B*a))/b^4)*(A*b - 3*B*a)*1i)/b^4)/((16*(108*B^3*a^12 - 12*A^3*a*b^11 - 54*B^3*a^11*b - 24*A^3*a^2*b^10 + 34*A^3*a^3*b^9 + 26*A^3*a^4*b^8 - 36*A^3*a^5*b^7 - 13*A^3*a^6*b^6 + 18*A^3*a^7*b^5 + 2*A^3*a^8*b^4 - 4*A^3*a^9*b^3 + 216*B^3*a^4*b^8 + 216*B^3*a^5*b^7 - 702*B^3*a^6*b^6 - 378*B^3*a^7*b^5 + 864*B^3*a^8*b^4 + 243*B^3*a^9*b^3 - 486*B^3*a^10*b^2 - 108*A*B^2*a^11*b - 252*A*B^2*a^3*b^9 - 324*A*B^2*a^4*b^8 + 774*A*B^2*a^5*b^7 + 486*A*B^2*a^6*b^6 - 900*A*B^2*a^7*b^5 - 279*A*B^2*a^8*b^4 + 486*A*B^2*a^9*b^3 + 54*A*B^2*a^10*b^2 + 96*A^2*B*a^2*b^10 + 156*A^2*B*a^3*b^9 - 282*A^2*B*a^4*b^8 - 198*A^2*B*a^5*b^7 + 312*A^2*B*a^6*b^6 + 105*A^2*B*a^7*b^5 - 162*A^2*B*a^8*b^4 - 18*A^2*B*a^9*b^3 + 36*A^2*B*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) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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)*(A*b - 3*B*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)))*(A*b - 3*B*a))/b^4)*(A*b - 3*B*a))/b^4 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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)*(A*b - 3*B*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)))*(A*b - 3*B*a))/b^4)*(A*b - 3*B*a))/b^4))*(A*b - 3*B*a)*2i)/(b^4*d) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*B^3*a^12 - 12*A^3*a*b^11 - 54*B^3*a^11*b - 24*A^3*a^2*b^10 + 34*A^3*a^3*b^9 + 26*A^3*a^4*b^8 - 36*A^3*a^5*b^7 - 13*A^3*a^6*b^6 + 18*A^3*a^7*b^5 + 2*A^3*a^8*b^4 - 4*A^3*a^9*b^3 + 216*B^3*a^4*b^8 + 216*B^3*a^5*b^7 - 702*B^3*a^6*b^6 - 378*B^3*a^7*b^5 + 864*B^3*a^8*b^4 + 243*B^3*a^9*b^3 - 486*B^3*a^10*b^2 - 108*A*B^2*a^11*b - 252*A*B^2*a^3*b^9 - 324*A*B^2*a^4*b^8 + 774*A*B^2*a^5*b^7 + 486*A*B^2*a^6*b^6 - 900*A*B^2*a^7*b^5 - 279*A*B^2*a^8*b^4 + 486*A*B^2*a^9*b^3 + 54*A*B^2*a^10*b^2 + 96*A^2*B*a^2*b^10 + 156*A^2*B*a^3*b^9 - 282*A^2*B*a^4*b^8 - 198*A^2*B*a^5*b^7 + 312*A^2*B*a^6*b^6 + 105*A^2*B*a^7*b^5 - 162*A^2*B*a^8*b^4 - 18*A^2*B*a^9*b^3 + 36*A^2*B*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*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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"
330,1,6899,220,11.530171,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}^3\,\left(2\,B\,a^4+A\,a^2\,b^2-6\,B\,a^2\,b^2+4\,A\,a\,b^3-B\,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\,B\,a^4-A\,a^2\,b^2-6\,B\,a^2\,b^2+4\,A\,a\,b^3+B\,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{B\,\mathrm{atan}\left(-\frac{\frac{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,B\,\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,B\,\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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(A^2\,B\,a^4\,b^5+4\,A^2\,B\,a^2\,b^7+4\,A^2\,B\,b^9-2\,A\,B^2\,a^7\,b^2-2\,A\,B^2\,a^6\,b^3+2\,A\,B^2\,a^5\,b^4+2\,A\,B^2\,a^3\,b^6+6\,A\,B^2\,a^2\,b^7-20\,A\,B^2\,a\,b^8-4\,A\,B^2\,b^9+4\,B^3\,a^9-2\,B^3\,a^8\,b-18\,B^3\,a^7\,b^2+13\,B^3\,a^6\,b^3+36\,B^3\,a^5\,b^4-26\,B^3\,a^4\,b^5-34\,B^3\,a^3\,b^6+24\,B^3\,a^2\,b^7+12\,B^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{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,B\,\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,B\,\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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(A^2\,B\,a^4\,b^5+4\,A^2\,B\,a^2\,b^7+4\,A^2\,B\,b^9-2\,A\,B^2\,a^7\,b^2-2\,A\,B^2\,a^6\,b^3+2\,A\,B^2\,a^5\,b^4+2\,A\,B^2\,a^3\,b^6+6\,A\,B^2\,a^2\,b^7-20\,A\,B^2\,a\,b^8-4\,A\,B^2\,b^9+4\,B^3\,a^9-2\,B^3\,a^8\,b-18\,B^3\,a^7\,b^2+13\,B^3\,a^6\,b^3+36\,B^3\,a^5\,b^4-26\,B^3\,a^4\,b^5-34\,B^3\,a^3\,b^6+24\,B^3\,a^2\,b^7+12\,B^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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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*B*a^4 + A*a^2*b^2 - 6*B*a^2*b^2 + 4*A*a*b^3 - B*a^3*b))/((a*b^2 - b^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*B*a^4 - A*a^2*b^2 - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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)) - (B*atan(-((B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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 - (B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*B^3*a^9 - 4*A*B^2*b^9 + 4*A^2*B*b^9 + 12*B^3*a*b^8 - 2*B^3*a^8*b + 24*B^3*a^2*b^7 - 34*B^3*a^3*b^6 - 26*B^3*a^4*b^5 + 36*B^3*a^5*b^4 + 13*B^3*a^6*b^3 - 18*B^3*a^7*b^2 - 20*A*B^2*a*b^8 + 6*A*B^2*a^2*b^7 + 2*A*B^2*a^3*b^6 + 2*A*B^2*a^5*b^4 - 2*A*B^2*a^6*b^3 - 2*A*B^2*a^7*b^2 + 4*A^2*B*a^2*b^7 + A^2*B*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) + (B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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 + (B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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(((((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)) + (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*B^3*a^9 - 4*A*B^2*b^9 + 4*A^2*B*b^9 + 12*B^3*a*b^8 - 2*B^3*a^8*b + 24*B^3*a^2*b^7 - 34*B^3*a^3*b^6 - 26*B^3*a^4*b^5 + 36*B^3*a^5*b^4 + 13*B^3*a^6*b^3 - 18*B^3*a^7*b^2 - 20*A*B^2*a*b^8 + 6*A*B^2*a^2*b^7 + 2*A*B^2*a^3*b^6 + 2*A*B^2*a^5*b^4 - 2*A*B^2*a^6*b^3 - 2*A*B^2*a^7*b^2 + 4*A^2*B*a^2*b^7 + A^2*B*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) - (((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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"
331,1,251,180,5.417375,"\text{Not used}","int((A + B/cos(c + d*x))/(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(B\,a^2-3\,A\,a\,b+2\,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\,A\,a^2+2\,A\,b^2-B\,a^2+A\,a\,b-4\,B\,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\,A\,a^2+2\,A\,b^2+B\,a^2-A\,a\,b-4\,B\,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)))*(B*a^2 + 2*B*b^2 - 3*A*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((tan(c/2 + (d*x)/2)^3*(2*A*a^2 + 2*A*b^2 - B*a^2 + A*a*b - 4*B*a*b))/((a + b)^2*(a - b)) - (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 - A*a*b - 4*B*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"
332,1,251,164,5.351536,"\text{Not used}","int((A + B/cos(c + d*x))/(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(2\,A\,a^2-3\,B\,a\,b+A\,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-A\,b^2+2\,B\,b^2-4\,A\,a\,b+B\,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^2-4\,A\,a\,b-B\,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*A*a^2 + A*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 - A*b^2 + 2*B*b^2 - 4*A*a*b + B*a*b))/((a + b)^2*(a - b)) - (tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 - 4*A*a*b - B*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"
333,1,6909,205,11.785268,"\text{Not used}","int((A + B/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(2\,A\,b^4-6\,A\,a^2\,b^2+B\,a^2\,b^2-A\,a\,b^3+4\,B\,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^4-6\,A\,a^2\,b^2-B\,a^2\,b^2+A\,a\,b^3+4\,B\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^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{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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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{\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\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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{\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\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,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+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^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{\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\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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{\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\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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 + 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))/(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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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) - ((tan(c/2 + (d*x)/2)^3*(2*A*b^4 - 6*A*a^2*b^2 + B*a^2*b^2 - A*a*b^3 + 4*B*a^3*b))/((a^2*b - a^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^4 - 6*A*a^2*b^2 - B*a^2*b^2 + A*a*b^3 + 4*B*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(((((a + b)^5*(a - b)^5)^(1/2)*((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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)) + (((a + b)^5*(a - b)^5)^(1/2)*((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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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 + 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))/(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*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)*((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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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"
334,1,5530,290,9.730002,"\text{Not used}","int((cos(c + d*x)*(A + B/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)}^5\,\left(6\,A\,b^5-2\,A\,a^5-12\,A\,a^2\,b^3+4\,A\,a^3\,b^2+B\,a^2\,b^3+6\,B\,a^3\,b^2-3\,A\,a\,b^4+2\,A\,a^4\,b-2\,B\,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\,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+3\,A\,a\,b^4+2\,A\,a^4\,b-2\,B\,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\,A\,a^6-6\,A\,a^4\,b^2-5\,B\,a^3\,b^3+13\,A\,a^2\,b^4+2\,B\,a\,b^5-6\,A\,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\,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{b\,\mathrm{atan}\left(\frac{\frac{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}-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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,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}+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}-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\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\,\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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*A*b^5 - 2*A*a^5 - 12*A*a^2*b^3 + 4*A*a^3*b^2 + B*a^2*b^3 + 6*B*a^3*b^2 - 3*A*a*b^4 + 2*A*a^4*b - 2*B*a*b^4))/((a^3*b - a^4)*(a + b)^2) + (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 + 3*A*a*b^4 + 2*A*a^4*b - 2*B*a*b^4))/((a + b)*(a^5 - 2*a^4*b + a^3*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 + 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) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A^3*b^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 + 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))/(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*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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"
335,1,10586,393,14.170052,"\text{Not used}","int((cos(c + d*x)^2*(A + B/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)}^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+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+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+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^2-6\,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{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}+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}\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{\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\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(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)}{2\,a^5}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,a^5}+\frac{\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}+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}\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{\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\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(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)}{2\,a^5}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}+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}-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}\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{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}+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}\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{\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\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(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)}{2\,a^5}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)}{2\,a^5}+\frac{\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}+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}\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{\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\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(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)}{2\,a^5}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)}{2\,a^5}}\right)\,\left(1{}\mathrm{i}\,A\,a^2-6{}\mathrm{i}\,B\,a\,b+12{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^5\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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}-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}+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}-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}\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^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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 + 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 + 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 + 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 - 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(((((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) + (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*(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*a^2*1i + A*b^2*12i - B*a*b*6i))/(2*a^5))*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*1i)/(2*a^5) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) - (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*(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*a^2*1i + A*b^2*12i - B*a*b*6i))/(2*a^5))*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*1i)/(2*a^5))/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 - 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 - 2592*A^2*B*a*b^14 + 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))/(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^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) + (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*(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*a^2*1i + A*b^2*12i - B*a*b*6i))/(2*a^5))*(A*a^2*1i + A*b^2*12i - B*a*b*6i))/(2*a^5) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) - (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*(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*a^2*1i + A*b^2*12i - B*a*b*6i))/(2*a^5))*(A*a^2*1i + A*b^2*12i - B*a*b*6i))/(2*a^5)))*(A*a^2*1i + A*b^2*12i - B*a*b*6i)*1i)/(a^5*d) + (b^2*atan(((b^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*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^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*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 - 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 - 2592*A^2*B*a*b^14 + 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))/(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^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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^2*((a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*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"
336,1,13092,418,19.960869,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^5*(a + b/cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(12\,A\,a^2\,b^5-2\,B\,b^7-8\,B\,a^7+4\,A\,a^3\,b^4-6\,A\,a^4\,b^3-A\,a^5\,b^2+6\,B\,a^2\,b^5-26\,B\,a^3\,b^4-11\,B\,a^4\,b^3+24\,B\,a^5\,b^2+2\,A\,a^6\,b+2\,B\,a\,b^6+4\,B\,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)}^3\,\left(72\,B\,a^8+18\,B\,b^8+36\,A\,a^2\,b^6-96\,A\,a^3\,b^5-14\,A\,a^4\,b^4+59\,A\,a^5\,b^3+3\,A\,a^6\,b^2-72\,B\,a^2\,b^6-60\,B\,a^3\,b^5+273\,B\,a^4\,b^4+47\,B\,a^5\,b^3-236\,B\,a^6\,b^2-18\,A\,a^7\,b-12\,B\,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\,B\,a^8+18\,B\,b^8-36\,A\,a^2\,b^6-96\,A\,a^3\,b^5+14\,A\,a^4\,b^4+59\,A\,a^5\,b^3-3\,A\,a^6\,b^2-72\,B\,a^2\,b^6+60\,B\,a^3\,b^5+273\,B\,a^4\,b^4-47\,B\,a^5\,b^3-236\,B\,a^6\,b^2-18\,A\,a^7\,b+12\,B\,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(2\,B\,b^7-8\,B\,a^7+12\,A\,a^2\,b^5-4\,A\,a^3\,b^4-6\,A\,a^4\,b^3+A\,a^5\,b^2-6\,B\,a^2\,b^5-26\,B\,a^3\,b^4+11\,B\,a^4\,b^3+24\,B\,a^5\,b^2+2\,A\,a^6\,b+2\,B\,a\,b^6-4\,B\,a^6\,b\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}}{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{\left(A\,b-4\,B\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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(A\,b-4\,B\,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)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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}}\right)\,\left(A\,b-4\,B\,a\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(\frac{\left(A\,b-4\,B\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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(A\,b-4\,B\,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)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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}}\right)\,\left(A\,b-4\,B\,a\right)\,1{}\mathrm{i}}{b^5}}{\frac{\left(\frac{\left(A\,b-4\,B\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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(A\,b-4\,B\,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)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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}}\right)\,\left(A\,b-4\,B\,a\right)}{b^5}-\frac{16\,\left(-4\,A^3\,a^{13}\,b^3+2\,A^3\,a^{12}\,b^4+26\,A^3\,a^{11}\,b^5-11\,A^3\,a^{10}\,b^6-70\,A^3\,a^9\,b^7+34\,A^3\,a^8\,b^8+110\,A^3\,a^7\,b^9-66\,A^3\,a^6\,b^{10}-110\,A^3\,a^5\,b^{11}+64\,A^3\,a^4\,b^{12}+64\,A^3\,a^3\,b^{13}-48\,A^3\,a^2\,b^{14}-16\,A^3\,a\,b^{15}+48\,A^2\,B\,a^{14}\,b^2-24\,A^2\,B\,a^{13}\,b^3-312\,A^2\,B\,a^{12}\,b^4+138\,A^2\,B\,a^{11}\,b^5+846\,A^2\,B\,a^{10}\,b^6-408\,A^2\,B\,a^9\,b^7-1314\,A^2\,B\,a^8\,b^8+726\,A^2\,B\,a^7\,b^9+1266\,A^2\,B\,a^6\,b^{10}-690\,A^2\,B\,a^5\,b^{11}-702\,A^2\,B\,a^4\,b^{12}+408\,A^2\,B\,a^3\,b^{13}+168\,A^2\,B\,a^2\,b^{14}-192\,A\,B^2\,a^{15}\,b+96\,A\,B^2\,a^{14}\,b^2+1248\,A\,B^2\,a^{13}\,b^3-576\,A\,B^2\,a^{12}\,b^4-3408\,A\,B^2\,a^{11}\,b^5+1632\,A\,B^2\,a^{10}\,b^6+5232\,A\,B^2\,a^9\,b^7-2649\,A\,B^2\,a^8\,b^8-4848\,A\,B^2\,a^7\,b^9+2376\,A\,B^2\,a^6\,b^{10}+2544\,A\,B^2\,a^5\,b^{11}-1104\,A\,B^2\,a^4\,b^{12}-576\,A\,B^2\,a^3\,b^{13}+256\,B^3\,a^{16}-128\,B^3\,a^{15}\,b-1664\,B^3\,a^{14}\,b^2+800\,B^3\,a^{13}\,b^3+4576\,B^3\,a^{12}\,b^4-2176\,B^3\,a^{11}\,b^5-6944\,B^3\,a^{10}\,b^6+3204\,B^3\,a^9\,b^7+6176\,B^3\,a^8\,b^8-2560\,B^3\,a^7\,b^9-3040\,B^3\,a^6\,b^{10}+960\,B^3\,a^5\,b^{11}+640\,B^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{\left(A\,b-4\,B\,a\right)\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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(A\,b-4\,B\,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)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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}}\right)\,\left(A\,b-4\,B\,a\right)}{b^5}}\right)\,\left(A\,b-4\,B\,a\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^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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{16\,\left(-4\,A^3\,a^{13}\,b^3+2\,A^3\,a^{12}\,b^4+26\,A^3\,a^{11}\,b^5-11\,A^3\,a^{10}\,b^6-70\,A^3\,a^9\,b^7+34\,A^3\,a^8\,b^8+110\,A^3\,a^7\,b^9-66\,A^3\,a^6\,b^{10}-110\,A^3\,a^5\,b^{11}+64\,A^3\,a^4\,b^{12}+64\,A^3\,a^3\,b^{13}-48\,A^3\,a^2\,b^{14}-16\,A^3\,a\,b^{15}+48\,A^2\,B\,a^{14}\,b^2-24\,A^2\,B\,a^{13}\,b^3-312\,A^2\,B\,a^{12}\,b^4+138\,A^2\,B\,a^{11}\,b^5+846\,A^2\,B\,a^{10}\,b^6-408\,A^2\,B\,a^9\,b^7-1314\,A^2\,B\,a^8\,b^8+726\,A^2\,B\,a^7\,b^9+1266\,A^2\,B\,a^6\,b^{10}-690\,A^2\,B\,a^5\,b^{11}-702\,A^2\,B\,a^4\,b^{12}+408\,A^2\,B\,a^3\,b^{13}+168\,A^2\,B\,a^2\,b^{14}-192\,A\,B^2\,a^{15}\,b+96\,A\,B^2\,a^{14}\,b^2+1248\,A\,B^2\,a^{13}\,b^3-576\,A\,B^2\,a^{12}\,b^4-3408\,A\,B^2\,a^{11}\,b^5+1632\,A\,B^2\,a^{10}\,b^6+5232\,A\,B^2\,a^9\,b^7-2649\,A\,B^2\,a^8\,b^8-4848\,A\,B^2\,a^7\,b^9+2376\,A\,B^2\,a^6\,b^{10}+2544\,A\,B^2\,a^5\,b^{11}-1104\,A\,B^2\,a^4\,b^{12}-576\,A\,B^2\,a^3\,b^{13}+256\,B^3\,a^{16}-128\,B^3\,a^{15}\,b-1664\,B^3\,a^{14}\,b^2+800\,B^3\,a^{13}\,b^3+4576\,B^3\,a^{12}\,b^4-2176\,B^3\,a^{11}\,b^5-6944\,B^3\,a^{10}\,b^6+3204\,B^3\,a^9\,b^7+6176\,B^3\,a^8\,b^8-2560\,B^3\,a^7\,b^9-3040\,B^3\,a^6\,b^{10}+960\,B^3\,a^5\,b^{11}+640\,B^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{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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,"((tan(c/2 + (d*x)/2)^7*(12*A*a^2*b^5 - 2*B*b^7 - 8*B*a^7 + 4*A*a^3*b^4 - 6*A*a^4*b^3 - A*a^5*b^2 + 6*B*a^2*b^5 - 26*B*a^3*b^4 - 11*B*a^4*b^3 + 24*B*a^5*b^2 + 2*A*a^6*b + 2*B*a*b^6 + 4*B*a^6*b))/(b^4*(a + b)^3*(a - b)) - (tan(c/2 + (d*x)/2)^3*(72*B*a^8 + 18*B*b^8 + 36*A*a^2*b^6 - 96*A*a^3*b^5 - 14*A*a^4*b^4 + 59*A*a^5*b^3 + 3*A*a^6*b^2 - 72*B*a^2*b^6 - 60*B*a^3*b^5 + 273*B*a^4*b^4 + 47*B*a^5*b^3 - 236*B*a^6*b^2 - 18*A*a^7*b - 12*B*a^7*b))/(3*b^4*(a + b)^2*(a - b)^3) + (tan(c/2 + (d*x)/2)^5*(72*B*a^8 + 18*B*b^8 - 36*A*a^2*b^6 - 96*A*a^3*b^5 + 14*A*a^4*b^4 + 59*A*a^5*b^3 - 3*A*a^6*b^2 - 72*B*a^2*b^6 + 60*B*a^3*b^5 + 273*B*a^4*b^4 - 47*B*a^5*b^3 - 236*B*a^6*b^2 - 18*A*a^7*b + 12*B*a^7*b))/(3*b^4*(a + b)^3*(a - b)^2) - (tan(c/2 + (d*x)/2)*(2*B*b^7 - 8*B*a^7 + 12*A*a^2*b^5 - 4*A*a^3*b^4 - 6*A*a^4*b^3 + A*a^5*b^2 - 6*B*a^2*b^5 - 26*B*a^3*b^4 + 11*B*a^4*b^3 + 24*B*a^5*b^2 + 2*A*a^6*b + 2*B*a*b^6 - 4*B*a^6*b))/(b^4*(a + b)*(a - b)^3))/(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((((((A*b - 4*B*a)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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)*(A*b - 4*B*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^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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))*(A*b - 4*B*a)*1i)/b^5 - ((((A*b - 4*B*a)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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)*(A*b - 4*B*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^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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))*(A*b - 4*B*a)*1i)/b^5)/(((((A*b - 4*B*a)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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)*(A*b - 4*B*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^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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))*(A*b - 4*B*a))/b^5 - (16*(256*B^3*a^16 - 16*A^3*a*b^15 - 128*B^3*a^15*b - 48*A^3*a^2*b^14 + 64*A^3*a^3*b^13 + 64*A^3*a^4*b^12 - 110*A^3*a^5*b^11 - 66*A^3*a^6*b^10 + 110*A^3*a^7*b^9 + 34*A^3*a^8*b^8 - 70*A^3*a^9*b^7 - 11*A^3*a^10*b^6 + 26*A^3*a^11*b^5 + 2*A^3*a^12*b^4 - 4*A^3*a^13*b^3 + 640*B^3*a^4*b^12 + 960*B^3*a^5*b^11 - 3040*B^3*a^6*b^10 - 2560*B^3*a^7*b^9 + 6176*B^3*a^8*b^8 + 3204*B^3*a^9*b^7 - 6944*B^3*a^10*b^6 - 2176*B^3*a^11*b^5 + 4576*B^3*a^12*b^4 + 800*B^3*a^13*b^3 - 1664*B^3*a^14*b^2 - 192*A*B^2*a^15*b - 576*A*B^2*a^3*b^13 - 1104*A*B^2*a^4*b^12 + 2544*A*B^2*a^5*b^11 + 2376*A*B^2*a^6*b^10 - 4848*A*B^2*a^7*b^9 - 2649*A*B^2*a^8*b^8 + 5232*A*B^2*a^9*b^7 + 1632*A*B^2*a^10*b^6 - 3408*A*B^2*a^11*b^5 - 576*A*B^2*a^12*b^4 + 1248*A*B^2*a^13*b^3 + 96*A*B^2*a^14*b^2 + 168*A^2*B*a^2*b^14 + 408*A^2*B*a^3*b^13 - 702*A^2*B*a^4*b^12 - 690*A^2*B*a^5*b^11 + 1266*A^2*B*a^6*b^10 + 726*A^2*B*a^7*b^9 - 1314*A^2*B*a^8*b^8 - 408*A^2*B*a^9*b^7 + 846*A^2*B*a^10*b^6 + 138*A^2*B*a^11*b^5 - 312*A^2*B*a^12*b^4 - 24*A^2*B*a^13*b^3 + 48*A^2*B*a^14*b^2))/(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) + ((((A*b - 4*B*a)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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)*(A*b - 4*B*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^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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))*(A*b - 4*B*a))/b^5))*(A*b - 4*B*a)*2i)/(b^5*d) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) - (a*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*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)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) + (a*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*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*B^3*a^16 - 16*A^3*a*b^15 - 128*B^3*a^15*b - 48*A^3*a^2*b^14 + 64*A^3*a^3*b^13 + 64*A^3*a^4*b^12 - 110*A^3*a^5*b^11 - 66*A^3*a^6*b^10 + 110*A^3*a^7*b^9 + 34*A^3*a^8*b^8 - 70*A^3*a^9*b^7 - 11*A^3*a^10*b^6 + 26*A^3*a^11*b^5 + 2*A^3*a^12*b^4 - 4*A^3*a^13*b^3 + 640*B^3*a^4*b^12 + 960*B^3*a^5*b^11 - 3040*B^3*a^6*b^10 - 2560*B^3*a^7*b^9 + 6176*B^3*a^8*b^8 + 3204*B^3*a^9*b^7 - 6944*B^3*a^10*b^6 - 2176*B^3*a^11*b^5 + 4576*B^3*a^12*b^4 + 800*B^3*a^13*b^3 - 1664*B^3*a^14*b^2 - 192*A*B^2*a^15*b - 576*A*B^2*a^3*b^13 - 1104*A*B^2*a^4*b^12 + 2544*A*B^2*a^5*b^11 + 2376*A*B^2*a^6*b^10 - 4848*A*B^2*a^7*b^9 - 2649*A*B^2*a^8*b^8 + 5232*A*B^2*a^9*b^7 + 1632*A*B^2*a^10*b^6 - 3408*A*B^2*a^11*b^5 - 576*A*B^2*a^12*b^4 + 1248*A*B^2*a^13*b^3 + 96*A*B^2*a^14*b^2 + 168*A^2*B*a^2*b^14 + 408*A^2*B*a^3*b^13 - 702*A^2*B*a^4*b^12 - 690*A^2*B*a^5*b^11 + 1266*A^2*B*a^6*b^10 + 726*A^2*B*a^7*b^9 - 1314*A^2*B*a^8*b^8 - 408*A^2*B*a^9*b^7 + 846*A^2*B*a^10*b^6 + 138*A^2*B*a^11*b^5 - 312*A^2*B*a^12*b^4 - 24*A^2*B*a^13*b^3 + 48*A^2*B*a^14*b^2))/(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) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) - (a*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) + (a*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*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"
337,1,9713,310,14.144521,"\text{Not used}","int((A + B/cos(c + d*x))/(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)\,\left(2\,B\,a^6+3\,A\,a^2\,b^4-2\,A\,a^3\,b^3+12\,B\,a^2\,b^4-4\,B\,a^3\,b^3-6\,B\,a^4\,b^2-6\,A\,a\,b^5+B\,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{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A\,a^2\,b^4-2\,B\,a^6+2\,A\,a^3\,b^3-12\,B\,a^2\,b^4-4\,B\,a^3\,b^3+6\,B\,a^4\,b^2+6\,A\,a\,b^5+B\,a^5\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-3\,B\,a^6+11\,B\,a^4\,b^2+A\,a^3\,b^3-18\,B\,a^2\,b^4+9\,A\,a\,b^5\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\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{\frac{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,B\,\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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,B\,\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(9\,A^2\,B\,a^4\,b^9+12\,A^2\,B\,a^2\,b^{11}+4\,A^2\,B\,b^{13}+6\,A\,B^2\,a^9\,b^4+6\,A\,B^2\,a^8\,b^5-20\,A\,B^2\,a^7\,b^6-14\,A\,B^2\,a^6\,b^7+14\,A\,B^2\,a^5\,b^8+6\,A\,B^2\,a^4\,b^9-22\,A\,B^2\,a^3\,b^{10}+6\,A\,B^2\,a^2\,b^{11}-28\,A\,B^2\,a\,b^{12}-4\,A\,B^2\,b^{13}+4\,B^3\,a^{13}-2\,B^3\,a^{12}\,b-26\,B^3\,a^{11}\,b^2+11\,B^3\,a^{10}\,b^3+70\,B^3\,a^9\,b^4-34\,B^3\,a^8\,b^5-110\,B^3\,a^7\,b^6+66\,B^3\,a^6\,b^7+110\,B^3\,a^5\,b^8-64\,B^3\,a^4\,b^9-64\,B^3\,a^3\,b^{10}+48\,B^3\,a^2\,b^{11}+16\,B^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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,B\,\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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,B\,\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(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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(9\,A^2\,B\,a^4\,b^9+12\,A^2\,B\,a^2\,b^{11}+4\,A^2\,B\,b^{13}+6\,A\,B^2\,a^9\,b^4+6\,A\,B^2\,a^8\,b^5-20\,A\,B^2\,a^7\,b^6-14\,A\,B^2\,a^6\,b^7+14\,A\,B^2\,a^5\,b^8+6\,A\,B^2\,a^4\,b^9-22\,A\,B^2\,a^3\,b^{10}+6\,A\,B^2\,a^2\,b^{11}-28\,A\,B^2\,a\,b^{12}-4\,A\,B^2\,b^{13}+4\,B^3\,a^{13}-2\,B^3\,a^{12}\,b-26\,B^3\,a^{11}\,b^2+11\,B^3\,a^{10}\,b^3+70\,B^3\,a^9\,b^4-34\,B^3\,a^8\,b^5-110\,B^3\,a^7\,b^6+66\,B^3\,a^6\,b^7+110\,B^3\,a^5\,b^8-64\,B^3\,a^4\,b^9-64\,B^3\,a^3\,b^{10}+48\,B^3\,a^2\,b^{11}+16\,B^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(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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*B*a^6 + 3*A*a^2*b^4 - 2*A*a^3*b^3 + 12*B*a^2*b^4 - 4*B*a^3*b^3 - 6*B*a^4*b^2 - 6*A*a*b^5 + B*a^5*b))/((a + b)*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) - (tan(c/2 + (d*x)/2)^5*(3*A*a^2*b^4 - 2*B*a^6 + 2*A*a^3*b^3 - 12*B*a^2*b^4 - 4*B*a^3*b^3 + 6*B*a^4*b^2 + 6*A*a*b^5 + B*a^5*b))/((a*b^3 - b^4)*(a + b)^3) + (4*tan(c/2 + (d*x)/2)^3*(A*a^3*b^3 - 3*B*a^6 - 18*B*a^2*b^4 + 11*B*a^4*b^2 + 9*A*a*b^5))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*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*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) + (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*B*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 + (B*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) - (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*B*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*B^3*a^13 - 4*A*B^2*b^13 + 4*A^2*B*b^13 + 16*B^3*a*b^12 - 2*B^3*a^12*b + 48*B^3*a^2*b^11 - 64*B^3*a^3*b^10 - 64*B^3*a^4*b^9 + 110*B^3*a^5*b^8 + 66*B^3*a^6*b^7 - 110*B^3*a^7*b^6 - 34*B^3*a^8*b^5 + 70*B^3*a^9*b^4 + 11*B^3*a^10*b^3 - 26*B^3*a^11*b^2 - 28*A*B^2*a*b^12 + 6*A*B^2*a^2*b^11 - 22*A*B^2*a^3*b^10 + 6*A*B^2*a^4*b^9 + 14*A*B^2*a^5*b^8 - 14*A*B^2*a^6*b^7 - 20*A*B^2*a^7*b^6 + 6*A*B^2*a^8*b^5 + 6*A*B^2*a^9*b^4 + 12*A^2*B*a^2*b^11 + 9*A^2*B*a^4*b^9))/(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) + (B*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) + (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*B*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 - (B*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) - (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*B*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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*B^3*a^13 - 4*A*B^2*b^13 + 4*A^2*B*b^13 + 16*B^3*a*b^12 - 2*B^3*a^12*b + 48*B^3*a^2*b^11 - 64*B^3*a^3*b^10 - 64*B^3*a^4*b^9 + 110*B^3*a^5*b^8 + 66*B^3*a^6*b^7 - 110*B^3*a^7*b^6 - 34*B^3*a^8*b^5 + 70*B^3*a^9*b^4 + 11*B^3*a^10*b^3 - 26*B^3*a^11*b^2 - 28*A*B^2*a*b^12 + 6*A*B^2*a^2*b^11 - 22*A*B^2*a^3*b^10 + 6*A*B^2*a^4*b^9 + 14*A*B^2*a^5*b^8 - 14*A*B^2*a^6*b^7 - 20*A*B^2*a^7*b^6 + 6*A*B^2*a^8*b^5 + 6*A*B^2*a^9*b^4 + 12*A^2*B*a^2*b^11 + 9*A^2*B*a^4*b^9))/(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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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"
338,1,439,274,6.798701,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^3*(a + b/cos(c + d*x))^4),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-B\,a^3+7\,A\,a^2\,b-9\,B\,a\,b^2+3\,A\,b^3\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(A\,a^3+2\,A\,b^3-2\,B\,a^3+2\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2-3\,B\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^3-2\,A\,b^3+2\,B\,a^3+2\,A\,a\,b^2-6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,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{\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\,a^3-3\,B\,a^2\,b+4\,A\,a\,b^2-2\,B\,b^3\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((4*tan(c/2 + (d*x)/2)^3*(3*A*b^3 - B*a^3 + 7*A*a^2*b - 9*B*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) - (tan(c/2 + (d*x)/2)^5*(A*a^3 + 2*A*b^3 - 2*B*a^3 + 2*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 - 3*B*a^2*b))/((a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(A*a^3 - 2*A*b^3 + 2*B*a^3 + 2*A*a*b^2 - 6*A*a^2*b + 6*B*a*b^2 - 3*B*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))) + (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*a^3 - 2*B*b^3 + 4*A*a*b^2 - 3*B*a^2*b))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
339,1,451,263,6.646450,"\text{Not used}","int((A + B/cos(c + d*x))/(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+6\,A\,a\,b^2-2\,A\,a^2\,b+2\,B\,a\,b^2-6\,B\,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^3-7\,B\,a^2\,b+7\,A\,a\,b^2-3\,B\,b^3\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+6\,A\,a\,b^2+2\,A\,a^2\,b-2\,B\,a\,b^2-6\,B\,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(-B\,a^3+4\,A\,a^2\,b-4\,B\,a\,b^2+A\,b^3\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 + 6*A*a*b^2 - 2*A*a^2*b + 2*B*a*b^2 - 6*B*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 + 7*A*a*b^2 - 7*B*a^2*b))/(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 + 6*A*a*b^2 + 2*A*a^2*b - 2*B*a*b^2 - 6*B*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 + 4*A*a^2*b - 4*B*a*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
340,1,439,237,6.673225,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + b/cos(c + d*x))^4),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-3\,B\,a^3+9\,A\,a^2\,b-7\,B\,a\,b^2+A\,b^3\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\,B\,a^3-2\,A\,b^3+B\,b^3-3\,A\,a\,b^2-6\,A\,a^2\,b+6\,B\,a\,b^2+2\,B\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-2\,B\,a^3+B\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2+2\,B\,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{\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^3-4\,B\,a^2\,b+3\,A\,a\,b^2-B\,b^3\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((4*tan(c/2 + (d*x)/2)^3*(A*b^3 - 3*B*a^3 + 9*A*a^2*b - 7*B*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*B*a^3 - 2*A*b^3 + B*b^3 - 3*A*a*b^2 - 6*A*a^2*b + 6*B*a*b^2 + 2*B*a^2*b))/((a + b)^3*(a - b)) - (tan(c/2 + (d*x)/2)*(2*A*b^3 - 2*B*a^3 + B*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 + 2*B*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))) + (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 + 3*A*a*b^2 - 4*B*a^2*b))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
341,1,9721,292,14.413947,"\text{Not used}","int((A + B/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(6\,A\,a^2\,b^4-2\,A\,b^6-4\,A\,a^3\,b^3-12\,A\,a^4\,b^2+2\,B\,a^3\,b^3+3\,B\,a^4\,b^2+A\,a\,b^5+6\,B\,a^5\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^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+A\,a\,b^5-6\,B\,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(9\,B\,a^5\,b-18\,A\,a^4\,b^2+B\,a^3\,b^3+11\,A\,a^2\,b^4-3\,A\,b^6\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\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{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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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{\mathrm{atan}\left(\frac{\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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{\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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\,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+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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{\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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(2\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,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,"((tan(c/2 + (d*x)/2)^5*(6*A*a^2*b^4 - 2*A*b^6 - 4*A*a^3*b^3 - 12*A*a^4*b^2 + 2*B*a^3*b^3 + 3*B*a^4*b^2 + A*a*b^5 + 6*B*a^5*b))/((a^3*b - a^4)*(a + b)^3) - (tan(c/2 + (d*x)/2)*(2*A*b^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 + A*a*b^5 - 6*B*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*(11*A*a^2*b^4 - 3*A*b^6 - 18*A*a^4*b^2 + B*a^3*b^3 + 9*B*a^5*b))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)))/(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))) - (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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 + 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^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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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) + (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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 + 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^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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 - 8*A*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"
342,1,7863,411,14.202666,"\text{Not used}","int((cos(c + d*x)*(A + B/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)\,\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^2-4\,A\,a\,b^6+2\,A\,a^6\,b+2\,B\,a\,b^6\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^2-12\,A\,a\,b^7-18\,B\,a\,b^7\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)}^7\,\left(24\,A\,a^2\,b^5-8\,A\,b^7-2\,A\,a^7-11\,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+4\,A\,a\,b^6+2\,A\,a^6\,b+2\,B\,a\,b^6\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)}^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+12\,A\,a\,b^7-18\,B\,a\,b^7\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{b\,\mathrm{atan}\left(\frac{\frac{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}-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}+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}\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{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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\,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\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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{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}-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}+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}\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{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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\,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\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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}+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}-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}\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{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}-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}+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}\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{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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\,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\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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{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}-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}+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}\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{b\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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\,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\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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,"(log(tan(c/2 + (d*x)/2) - 1i)*(4*A*b - B*a)*1i)/(a^5*d) - ((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 - 4*A*a*b^6 + 2*A*a^6*b + 2*B*a*b^6))/((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 - 12*A*a*b^7 - 18*B*a*b^7))/(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)^7*(24*A*a^2*b^5 - 8*A*b^7 - 2*A*a^7 - 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 + 4*A*a*b^6 + 2*A*a^6*b + 2*B*a*b^6))/((a^4*b - a^5)*(a + b)^3) + (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 + 12*A*a*b^7 - 18*B*a*b^7))/(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)*(A*b*4i - B*a*1i))/(a^5*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*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)) + (b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) - (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*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 - 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 + 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))/(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) + (b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) + (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)) - (b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) - (b*((a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*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"
343,1,14438,538,15.817291,"\text{Not used}","int((cos(c + d*x)^2*(A + B/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)\,\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+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}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^{10}-18\,B\,a^9\,b+36\,A\,a^8\,b^2+132\,B\,a^7\,b^3-324\,A\,a^6\,b^4-320\,B\,a^5\,b^5+740\,A\,a^4\,b^6+248\,B\,a^3\,b^7-611\,A\,a^2\,b^8-72\,B\,a\,b^9+180\,A\,b^{10}\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)}^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^2-10\,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^2-30\,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^2-30\,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}}{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}-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}\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}-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^2-32\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\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(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)}{2\,a^6}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}-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}\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}-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^2-32\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\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(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)}{2\,a^6}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}-20\,A^2\,B\,a^{17}\,b^2+20\,A^2\,B\,a^{16}\,b^3-1345\,A^2\,B\,a^{15}\,b^4-255\,A^2\,B\,a^{14}\,b^5-13929\,A^2\,B\,a^{13}\,b^6-24711\,A^2\,B\,a^{12}\,b^7+88721\,A^2\,B\,a^{11}\,b^8+77359\,A^2\,B\,a^{10}\,b^9-201479\,A^2\,B\,a^9\,b^{10}-105755\,A^2\,B\,a^8\,b^{11}+241596\,A^2\,B\,a^7\,b^{12}+76812\,A^2\,B\,a^6\,b^{13}-165384\,A^2\,B\,a^5\,b^{14}-29520\,A^2\,B\,a^4\,b^{15}+61440\,A^2\,B\,a^3\,b^{16}+4800\,A^2\,B\,a^2\,b^{17}-9600\,A^2\,B\,a\,b^{18}+320\,A\,B^2\,a^{16}\,b^3+80\,A\,B^2\,a^{15}\,b^4+7440\,A\,B^2\,a^{14}\,b^5+11960\,A\,B^2\,a^{13}\,b^6-40368\,A\,B^2\,a^{12}\,b^7-34567\,A\,B^2\,a^{11}\,b^8+86512\,A\,B^2\,a^{10}\,b^9+45148\,A\,B^2\,a^9\,b^{10}-100368\,A\,B^2\,a^8\,b^{11}-31680\,A\,B^2\,a^7\,b^{12}+67392\,A\,B^2\,a^6\,b^{13}+11904\,A\,B^2\,a^5\,b^{14}-24768\,A\,B^2\,a^4\,b^{15}-1920\,A\,B^2\,a^3\,b^{16}+3840\,A\,B^2\,a^2\,b^{17}-1280\,B^3\,a^{15}\,b^4-1920\,B^3\,a^{14}\,b^5+6080\,B^3\,a^{13}\,b^6+5120\,B^3\,a^{12}\,b^7-12352\,B^3\,a^{11}\,b^8-6408\,B^3\,a^{10}\,b^9+13888\,B^3\,a^9\,b^{10}+4352\,B^3\,a^8\,b^{11}-9152\,B^3\,a^7\,b^{12}-1600\,B^3\,a^6\,b^{13}+3328\,B^3\,a^5\,b^{14}+256\,B^3\,a^4\,b^{15}-512\,B^3\,a^3\,b^{16}\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(\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}-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}\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}-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^2-32\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\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(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)}{2\,a^6}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)}{2\,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}-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}\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}-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^2-32\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\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(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)}{2\,a^6}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)}{2\,a^6}}\right)\,\left(1{}\mathrm{i}\,A\,a^2-8{}\mathrm{i}\,B\,a\,b+20{}\mathrm{i}\,A\,b^2\right)\,1{}\mathrm{i}}{a^6\,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(-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}-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}\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^2\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,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^2-32\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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^2\,\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}-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}\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^2\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,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^2-32\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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{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}-20\,A^2\,B\,a^{17}\,b^2+20\,A^2\,B\,a^{16}\,b^3-1345\,A^2\,B\,a^{15}\,b^4-255\,A^2\,B\,a^{14}\,b^5-13929\,A^2\,B\,a^{13}\,b^6-24711\,A^2\,B\,a^{12}\,b^7+88721\,A^2\,B\,a^{11}\,b^8+77359\,A^2\,B\,a^{10}\,b^9-201479\,A^2\,B\,a^9\,b^{10}-105755\,A^2\,B\,a^8\,b^{11}+241596\,A^2\,B\,a^7\,b^{12}+76812\,A^2\,B\,a^6\,b^{13}-165384\,A^2\,B\,a^5\,b^{14}-29520\,A^2\,B\,a^4\,b^{15}+61440\,A^2\,B\,a^3\,b^{16}+4800\,A^2\,B\,a^2\,b^{17}-9600\,A^2\,B\,a\,b^{18}+320\,A\,B^2\,a^{16}\,b^3+80\,A\,B^2\,a^{15}\,b^4+7440\,A\,B^2\,a^{14}\,b^5+11960\,A\,B^2\,a^{13}\,b^6-40368\,A\,B^2\,a^{12}\,b^7-34567\,A\,B^2\,a^{11}\,b^8+86512\,A\,B^2\,a^{10}\,b^9+45148\,A\,B^2\,a^9\,b^{10}-100368\,A\,B^2\,a^8\,b^{11}-31680\,A\,B^2\,a^7\,b^{12}+67392\,A\,B^2\,a^6\,b^{13}+11904\,A\,B^2\,a^5\,b^{14}-24768\,A\,B^2\,a^4\,b^{15}-1920\,A\,B^2\,a^3\,b^{16}+3840\,A\,B^2\,a^2\,b^{17}-1280\,B^3\,a^{15}\,b^4-1920\,B^3\,a^{14}\,b^5+6080\,B^3\,a^{13}\,b^6+5120\,B^3\,a^{12}\,b^7-12352\,B^3\,a^{11}\,b^8-6408\,B^3\,a^{10}\,b^9+13888\,B^3\,a^9\,b^{10}+4352\,B^3\,a^8\,b^{11}-9152\,B^3\,a^7\,b^{12}-1600\,B^3\,a^6\,b^{13}+3328\,B^3\,a^5\,b^{14}+256\,B^3\,a^4\,b^{15}-512\,B^3\,a^3\,b^{16}\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{b^2\,\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}-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}\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^2\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,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^2-32\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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^2\,\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}-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}\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^2\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,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^2-32\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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 + 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 + 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) + (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 - 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)^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 - 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 - 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 - 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))/(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)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*(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*a^2*1i + A*b^2*20i - B*a*b*8i))/(2*a^6))*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*1i)/(2*a^6) + (((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*(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*a^2*1i + A*b^2*20i - B*a*b*8i))/(2*a^6))*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*1i)/(2*a^6))/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 - 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 - 9600*A^2*B*a*b^18 + 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))/(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)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*(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*a^2*1i + A*b^2*20i - B*a*b*8i))/(2*a^6))*(A*a^2*1i + A*b^2*20i - B*a*b*8i))/(2*a^6) - (((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*(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*a^2*1i + A*b^2*20i - B*a*b*8i))/(2*a^6))*(A*a^2*1i + A*b^2*20i - B*a*b*8i))/(2*a^6)))*(A*a^2*1i + A*b^2*20i - B*a*b*8i)*1i)/(a^6*d) - (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*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^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*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 - 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 - 9600*A^2*B*a*b^18 + 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))/(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^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*((a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*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"
344,1,91,61,2.559412,"\text{Not used}","int((B/cos(c + d*x) + (B*b)/a)/(a + b/cos(c + d*x)),x)","\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)}{a^2\,d}+\frac{2\,B\,\mathrm{atanh}\left(\frac{\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)\,\left(a+b\right)}\right)\,\sqrt{a^2-b^2}}{a^2\,d}","Not used",1,"(2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d) + (2*B*atanh((sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a + b)))*(a^2 - b^2)^(1/2))/(a^2*d)","B"
345,1,6,6,2.231245,"\text{Not used}","int((B/cos(c + d*x) + (B*a)/b)/(a + b/cos(c + d*x)),x)","\frac{B\,x}{b}","Not used",1,"(B*x)/b","B"
346,1,444,86,2.574419,"\text{Not used}","int((a + b/cos(c + d*x))/(b + a/cos(c + d*x))^2,x)","\frac{2\,\mathrm{atanh}\left(\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{64\,a^4-128\,a^3\,b+128\,a\,b^3-64\,b^4}-\frac{192\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b^2-128\,a^3-64\,b^3+\frac{64\,a^4}{b}}+\frac{192\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b-64\,b^2-\frac{128\,a^3}{b}+\frac{64\,a^4}{b^2}}-\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b-64\,b^2-\frac{128\,a^3}{b}+\frac{64\,a^4}{b^2}}\right)\,\sqrt{b^2-a^2}}{b^2\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{64\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b-64\,a^2-\frac{64\,a^3}{b}+\frac{64\,a^4}{b^2}}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b^2-64\,a^2\,b-64\,a^3+\frac{64\,a^4}{b}}-\frac{64\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^4-64\,a^3\,b-64\,a^2\,b^2+64\,a\,b^3}-\frac{64\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b-64\,a^2-\frac{64\,a^3}{b}+\frac{64\,a^4}{b^2}}\right)}{b^2\,d}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b\,d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*atanh((64*a^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b^3 - 128*a^3*b + 64*a^4 - 64*b^4) - (192*a^2*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b^2 - 128*a^3 - 64*b^3 + (64*a^4)/b) + (192*a*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b - 64*b^2 - (128*a^3)/b + (64*a^4)/b^2) - (64*b*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b - 64*b^2 - (128*a^3)/b + (64*a^4)/b^2))*(b^2 - a^2)^(1/2))/(b^2*d) - (2*a*atan((64*a^2*tan(c/2 + (d*x)/2))/(64*a*b - 64*a^2 - (64*a^3)/b + (64*a^4)/b^2) + (64*a^3*tan(c/2 + (d*x)/2))/(64*a*b^2 - 64*a^2*b - 64*a^3 + (64*a^4)/b) - (64*a^4*tan(c/2 + (d*x)/2))/(64*a*b^3 - 64*a^3*b + 64*a^4 - 64*a^2*b^2) - (64*a*b*tan(c/2 + (d*x)/2))/(64*a*b - 64*a^2 - (64*a^3)/b + (64*a^4)/b^2)))/(b^2*d) - (2*a*tan(c/2 + (d*x)/2))/(b*d*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
347,1,26,87,2.297651,"\text{Not used}","int(-(1/cos(c + d*x) + 3)/(1/cos(c + d*x) - 2),x)","\frac{3\,x}{2}+\frac{5\,\sqrt{3}\,\mathrm{atanh}\left(\sqrt{3}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{3\,d}","Not used",1,"(3*x)/2 + (5*3^(1/2)*atanh(3^(1/2)*tan(c/2 + (d*x)/2)))/(3*d)","B"
348,0,-1,485,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^4, x)","F"
349,0,-1,397,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
350,0,-1,314,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
351,0,-1,256,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
352,0,-1,320,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2), x)","F"
353,0,-1,344,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(1/2), x)","F"
354,0,-1,429,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(1/2), x)","F"
355,0,-1,509,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2), x)","F"
356,0,-1,475,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
357,0,-1,388,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^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)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
358,0,-1,312,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
359,0,-1,381,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(3/2), x)","F"
360,0,-1,361,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(3/2), x)","F"
361,0,-1,428,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(3/2), x)","F"
362,0,-1,520,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2), x)","F"
363,0,-1,566,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
364,0,-1,469,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^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)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
365,0,-1,384,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
366,0,-1,442,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(5/2), x)","F"
367,0,-1,433,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(5/2), x)","F"
368,0,-1,450,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2), x)","F"
369,0,-1,518,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2), x)","F"
370,0,-1,617,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2), x)","F"
371,0,-1,329,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/2)), x)","F"
372,0,-1,261,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/2)), x)","F"
373,0,-1,210,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/2)), x)","F"
374,0,-1,208,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{A+\frac{B}{\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))/(a + b/cos(c + d*x))^(1/2), x)","F"
375,0,-1,348,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(1/2), x)","F"
376,0,-1,435,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(1/2), x)","F"
377,0,-1,525,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + b/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)}\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + b/cos(c + d*x))^(1/2), x)","F"
378,0,-1,329,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(3/2)), x)","F"
379,0,-1,275,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(3/2)), x)","F"
380,0,-1,254,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(a + b/cos(c + d*x))^(3/2)), x)","F"
381,0,-1,376,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{A+\frac{B}{\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))/(a + b/cos(c + d*x))^(3/2), x)","F"
382,0,-1,427,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(3/2), x)","F"
383,0,-1,531,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(3/2), x)","F"
384,0,-1,630,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B/cos(c + d*x)))/(a + b/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)}\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 + B/cos(c + d*x)))/(a + b/cos(c + d*x))^(3/2), x)","F"
385,0,-1,510,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4\,{\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))/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2)), x)","F"
386,0,-1,417,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)), x)","F"
387,0,-1,387,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/2)), x)","F"
388,0,-1,353,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/2)), x)","F"
389,0,-1,495,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{A+\frac{B}{\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))/(a + b/cos(c + d*x))^(5/2), x)","F"
390,0,-1,582,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(5/2), x)","F"
391,0,-1,686,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B/cos(c + d*x)))/(a + b/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)}\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 + B/cos(c + d*x)))/(a + b/cos(c + d*x))^(5/2), x)","F"
392,0,-1,105,0.000000,"\text{Not used}","int((A + A/cos(e + f*x))/(cos(e + f*x)*(a + b/cos(e + f*x))^(1/2)),x)","\int \frac{A+\frac{A}{\cos\left(e+f\,x\right)}}{\cos\left(e+f\,x\right)\,\sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((A + A/cos(e + f*x))/(cos(e + f*x)*(a + b/cos(e + f*x))^(1/2)), x)","F"
393,0,-1,107,0.000000,"\text{Not used}","int((A - A/cos(e + f*x))/(cos(e + f*x)*(a + b/cos(e + f*x))^(1/2)),x)","\int \frac{A-\frac{A}{\cos\left(e+f\,x\right)}}{\cos\left(e+f\,x\right)\,\sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((A - A/cos(e + f*x))/(cos(e + f*x)*(a + b/cos(e + f*x))^(1/2)), x)","F"
394,0,-1,180,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2), x)","F"
395,0,-1,143,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2), x)","F"
396,0,-1,111,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/(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)}\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)))/(1/cos(c + d*x))^(1/2), x)","F"
397,0,-1,115,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/(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)}\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)))/(1/cos(c + d*x))^(3/2), x)","F"
398,0,-1,148,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/(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)}\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)))/(1/cos(c + d*x))^(5/2), x)","F"
399,0,-1,180,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x)))/(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)}\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)))/(1/cos(c + d*x))^(7/2), x)","F"
400,0,-1,263,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2), x)","F"
401,0,-1,221,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2), x)","F"
402,0,-1,177,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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)}\right)}^2}{\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))^2)/(1/cos(c + d*x))^(1/2), x)","F"
403,0,-1,161,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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)}\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))*(a + b/cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2), x)","F"
404,0,-1,171,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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)}\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))*(a + b/cos(c + d*x))^2)/(1/cos(c + d*x))^(5/2), x)","F"
405,0,-1,213,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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)}\right)}^2}{{\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))^2)/(1/cos(c + d*x))^(7/2), x)","F"
406,0,-1,254,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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)}\right)}^2}{{\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))^2)/(1/cos(c + d*x))^(9/2), x)","F"
407,0,-1,345,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2), x)","F"
408,0,-1,295,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2), x)","F"
409,0,-1,244,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3)/(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)}\right)}^3}{\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))^3)/(1/cos(c + d*x))^(1/2), x)","F"
410,0,-1,239,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3)/(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)}\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))*(a + b/cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2), x)","F"
411,0,-1,236,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3)/(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)}\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))*(a + b/cos(c + d*x))^3)/(1/cos(c + d*x))^(5/2), x)","F"
412,0,-1,245,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3)/(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)}\right)}^3}{{\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))^3)/(1/cos(c + d*x))^(7/2), x)","F"
413,0,-1,295,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3)/(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)}\right)}^3}{{\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))^3)/(1/cos(c + d*x))^(9/2), x)","F"
414,0,-1,345,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3)/(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)}\right)}^3}{{\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))^3)/(1/cos(c + d*x))^(11/2), x)","F"
415,0,-1,277,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b/cos(c + d*x)), x)","F"
416,0,-1,210,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{a+\frac{b}{\cos\left(c+d\,x\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)), x)","F"
417,0,-1,126,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{a+\frac{b}{\cos\left(c+d\,x\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)), x)","F"
418,0,-1,101,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x)),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{a+\frac{b}{\cos\left(c+d\,x\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)), x)","F"
419,0,-1,149,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
420,0,-1,196,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
421,0,-1,242,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(5/2)), x)","F"
422,0,-1,406,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b/cos(c + d*x))^2,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b/cos(c + d*x))^2, x)","F"
423,0,-1,315,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b/cos(c + d*x))^2,x)","\int \frac{\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)}\right)}^2} \,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))^2, x)","F"
424,0,-1,257,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x))^2,x)","\int \frac{\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)}\right)}^2} \,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))^2, x)","F"
425,0,-1,263,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x))^2,x)","\int \frac{\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)}\right)}^2} \,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))^2, x)","F"
426,0,-1,283,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
427,0,-1,365,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
428,0,-1,583,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + b/cos(c + d*x))^3, x)","F"
429,0,-1,480,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b/cos(c + d*x))^3, x)","F"
430,0,-1,402,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\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)}\right)}^3} \,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))^3, x)","F"
431,0,-1,402,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\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)}\right)}^3} \,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))^3, x)","F"
432,0,-1,402,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x))^3,x)","\int \frac{\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)}\right)}^3} \,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))^3, x)","F"
433,0,-1,427,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
434,0,-1,521,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
435,0,-1,336,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2), x)","F"
436,0,-1,253,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2), x)","F"
437,0,-1,208,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
438,0,-1,201,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2), x)","F"
439,0,-1,267,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(5/2), x)","F"
440,0,-1,343,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(7/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\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))*(a + b/cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(7/2), x)","F"
441,0,-1,421,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2), x)","F"
442,0,-1,339,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2), x)","F"
443,0,-1,272,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/(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)}\right)}^{3/2}}{\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))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
444,0,-1,276,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/(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)}\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))*(a + b/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2), x)","F"
445,0,-1,266,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/(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)}\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))*(a + b/cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(5/2), x)","F"
446,0,-1,342,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/(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)}\right)}^{3/2}}{{\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))^(3/2))/(1/cos(c + d*x))^(7/2), x)","F"
447,0,-1,427,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/(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)}\right)}^{3/2}}{{\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))^(3/2))/(1/cos(c + d*x))^(9/2), x)","F"
448,0,-1,513,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2), x)","F"
449,0,-1,422,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2), x)","F"
450,0,-1,359,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/(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)}\right)}^{5/2}}{\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))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
451,0,-1,349,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/(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)}\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))*(a + b/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)","F"
452,0,-1,342,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/(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)}\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))*(a + b/cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(5/2), x)","F"
453,0,-1,340,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/(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)}\right)}^{5/2}}{{\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))^(5/2))/(1/cos(c + d*x))^(7/2), x)","F"
454,0,-1,425,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/(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)}\right)}^{5/2}}{{\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))^(5/2))/(1/cos(c + d*x))^(9/2), x)","F"
455,0,-1,519,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/(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)}\right)}^{5/2}}{{\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))^(5/2))/(1/cos(c + d*x))^(11/2), x)","F"
456,0,-1,344,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\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))^(1/2), x)","F"
457,0,-1,256,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\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))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x))^(1/2), x)","F"
458,0,-1,138,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\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))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x))^(1/2), x)","F"
459,0,-1,150,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
460,0,-1,212,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
461,0,-1,280,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{\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))/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
462,0,-1,371,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\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)}\right)}^{3/2}} \,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))^(3/2), x)","F"
463,0,-1,220,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\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)}\right)}^{3/2}} \,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))^(3/2), x)","F"
464,0,-1,215,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\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)}\right)}^{3/2}} \,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))^(3/2), x)","F"
465,0,-1,235,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
466,0,-1,326,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
467,0,-1,423,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
468,0,-1,399,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\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)}\right)}^{5/2}} \,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))^(5/2), x)","F"
469,0,-1,329,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\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)}\right)}^{5/2}} \,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))^(5/2), x)","F"
470,0,-1,346,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{\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)}\right)}^{5/2}} \,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))^(5/2), x)","F"
471,0,-1,368,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
472,0,-1,472,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
473,0,-1,588,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/((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)}}{{\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))/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)), x)","F"
474,0,-1,126,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(2/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^(2/3), x)","F"
475,0,-1,126,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/3),x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\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))*(a + b/cos(c + d*x))^(1/3), x)","F"
476,0,-1,126,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + b/cos(c + d*x))^(1/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(a + b/cos(c + d*x))^(1/3), x)","F"
477,0,-1,126,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(a + b/cos(c + d*x))^(2/3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(a + b/cos(c + d*x))^(2/3), x)","F"
478,0,-1,36,0.000000,"\text{Not used}","int((A + B/cos(e + f*x))*(a + b/cos(e + f*x))^m*(c/cos(e + f*x))^n,x)","\int \left(A+\frac{B}{\cos\left(e+f\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",0,"int((A + B/cos(e + f*x))*(a + b/cos(e + f*x))^m*(c/cos(e + f*x))^n, x)","F"
479,0,-1,544,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^4*(1/cos(c + d*x))^m, x)","F"
480,0,-1,366,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^3*(1/cos(c + d*x))^m, x)","F"
481,0,-1,261,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2*(1/cos(c + d*x))^m, x)","F"
482,0,-1,177,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))*(1/cos(c + d*x))^m,x)","\int \left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m \,d x","Not used",1,"int((A + B/cos(c + d*x))*(a + b/cos(c + d*x))*(1/cos(c + d*x))^m, x)","F"
483,1,166,132,0.890797,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x)),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\,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*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"
484,1,128,101,0.358079,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(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\,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\,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*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"
485,1,85,70,2.660815,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(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\,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}","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","B"
486,1,96,66,3.059188,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(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\,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}}","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))","B"
487,1,150,95,3.293284,"\text{Not used}","int(((A + B/cos(c + d*x))*(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\,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\,B\,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*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*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*B*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"
488,1,177,132,3.553057,"\text{Not used}","int(((A + B/cos(c + d*x))*(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\,B\,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\,B\,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*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*B*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*B*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"
489,1,266,194,3.188645,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2,x)","\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\,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}}","Not used",1,"(2*B*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)^(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))","B"
490,1,231,161,3.011828,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + a/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\,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*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"
491,1,153,126,2.914976,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(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\,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\,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}}","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*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))","B"
492,1,134,116,3.161661,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(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\,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\,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}}","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*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))","B"
493,1,196,120,3.938073,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2,x)","\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,"(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"
494,1,229,159,4.152892,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/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{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)) + (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"
495,1,235,194,4.692086,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\frac{6\,A\,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\,A\,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\,A\,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\,B\,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\,B\,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\,B\,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}}","Not used",1,"(6*A*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*A*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*A*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*B*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 84*B*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*B*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))","B"
496,0,-1,157,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x)), x)","F"
497,0,-1,124,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x)), x)","F"
498,0,-1,88,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x)), x)","F"
499,0,-1,83,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))), x)","F"
500,0,-1,113,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))), x)","F"
501,0,-1,152,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))), x)","F"
502,0,-1,204,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^2, x)","F"
503,0,-1,171,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^2, x)","F"
504,0,-1,137,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^2, x)","F"
505,0,-1,121,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^2), x)","F"
506,0,-1,121,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^2), x)","F"
507,0,-1,164,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^2), x)","F"
508,0,-1,197,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^2), x)","F"
509,0,-1,221,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^3, x)","F"
510,0,-1,188,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^3, x)","F"
511,0,-1,182,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^3), x)","F"
512,0,-1,178,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3), x)","F"
513,0,-1,180,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3), x)","F"
514,0,-1,221,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3), x)","F"
515,0,-1,220,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2), x)","F"
516,0,-1,175,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
517,0,-1,130,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
518,0,-1,82,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
519,0,-1,96,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(1/2), x)","F"
520,0,-1,98,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
521,0,-1,151,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
522,0,-1,196,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2), x)","F"
523,0,-1,275,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2), x)","F"
524,0,-1,228,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2), x)","F"
525,0,-1,181,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2), x)","F"
526,0,-1,131,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
527,0,-1,145,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
528,0,-1,144,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(3/2), x)","F"
529,0,-1,153,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
530,0,-1,200,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
531,0,-1,247,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
532,0,-1,275,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2), x)","F"
533,0,-1,228,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2), x)","F"
534,0,-1,178,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2), x)","F"
535,0,-1,192,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(5/2), x)","F"
536,0,-1,197,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(5/2), x)","F"
537,0,-1,200,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + a/cos(c + d*x))^(5/2), x)","F"
538,0,-1,200,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
539,0,-1,247,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
540,0,-1,294,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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 + B/cos(c + d*x))*(a + a/cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
541,0,-1,250,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
542,0,-1,207,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
543,0,-1,162,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
544,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(1/2), x)","F"
545,0,-1,140,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
546,0,-1,181,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
547,0,-1,230,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(1/2)), x)","F"
548,0,-1,270,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(3/2), x)","F"
549,0,-1,223,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(3/2), x)","F"
550,0,-1,176,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(3/2), x)","F"
551,0,-1,127,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
552,0,-1,185,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
553,0,-1,237,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
554,0,-1,287,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\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))/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
555,0,-1,317,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(5/2), x)","F"
556,0,-1,270,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(5/2), x)","F"
557,0,-1,223,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + a/cos(c + d*x))^(5/2), x)","F"
558,0,-1,223,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
559,0,-1,176,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
560,0,-1,234,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
561,0,-1,286,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\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))/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
562,1,166,140,0.765440,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x)),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\,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*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"
563,1,128,108,0.622401,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x)),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\,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*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"
564,1,85,75,0.624361,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + b/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\,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}","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","B"
565,1,96,71,3.340774,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + b/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\,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}}","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))","B"
566,1,150,103,3.857963,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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\,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\,\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\,\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*ellipticF(c/2 + (d*x)/2, 2))/d + (2*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)) + (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*B*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"
567,1,177,140,4.300749,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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\,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\,B\,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\,B\,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)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\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*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*B*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*B*b*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"
568,1,229,182,3.170128,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\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\,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{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,"(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*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 - (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"
569,1,177,140,3.036706,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + b/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\,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{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}}","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*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 - (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))","B"
570,1,158,121,3.314245,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + b/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{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}}","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 + (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))","B"
571,1,194,126,4.273804,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2,x)","\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,"(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"
572,1,227,172,4.635407,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/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{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)) + (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"
573,1,233,214,4.975529,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\frac{6\,A\,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\,A\,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\,A\,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\,B\,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\,B\,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\,B\,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}}","Not used",1,"(6*A*b^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*A*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*B*b^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*B*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 84*B*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))","B"
574,0,-1,182,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x)), x)","F"
575,0,-1,136,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x)), x)","F"
576,0,-1,89,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x)), x)","F"
577,0,-1,61,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{\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))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))), x)","F"
578,0,-1,86,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))), x)","F"
579,0,-1,150,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\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))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))), x)","F"
580,0,-1,217,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))), x)","F"
581,0,-1,305,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^2, x)","F"
582,0,-1,223,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^2, x)","F"
583,0,-1,203,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^2), x)","F"
584,0,-1,197,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^2), x)","F"
585,0,-1,255,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^2), x)","F"
586,0,-1,346,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^2), x)","F"
587,0,-1,461,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^3, x)","F"
588,0,-1,367,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^3, x)","F"
589,0,-1,346,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^3), x)","F"
590,0,-1,338,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^3), x)","F"
591,0,-1,342,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^3), x)","F"
592,0,-1,420,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^3), x)","F"
593,0,-1,523,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^3), x)","F"
594,0,-1,343,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(1/2), x)","F"
595,0,-1,267,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(1/2), x)","F"
596,0,-1,201,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(1/2), x)","F"
597,0,-1,208,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(1/2), x)","F"
598,0,-1,253,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
599,0,-1,336,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
600,0,-1,427,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2), x)","F"
601,0,-1,342,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2), x)","F"
602,0,-1,266,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(3/2), x)","F"
603,0,-1,276,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(3/2), x)","F"
604,0,-1,272,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(3/2), x)","F"
605,0,-1,339,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/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)}\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
606,0,-1,421,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/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)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
607,0,-1,519,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{11/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(11/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2), x)","F"
608,0,-1,425,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2), x)","F"
609,0,-1,340,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2), x)","F"
610,0,-1,342,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(5/2), x)","F"
611,0,-1,349,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(5/2), x)","F"
612,0,-1,359,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+\frac{B}{\cos\left(c+d\,x\right)}\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))*(a + b/cos(c + d*x))^(5/2), x)","F"
613,0,-1,422,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/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)}\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
614,0,-1,513,0.000000,"\text{Not used}","int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/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)}\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B/cos(c + d*x))*(a + b/cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
615,0,-1,280,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(1/2), x)","F"
616,0,-1,212,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(1/2), x)","F"
617,0,-1,150,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(1/2), x)","F"
618,0,-1,138,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(1/2)), x)","F"
619,0,-1,256,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(1/2)), x)","F"
620,0,-1,344,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B/cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(1/2)), x)","F"
621,0,-1,423,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(3/2), x)","F"
622,0,-1,326,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(3/2), x)","F"
623,0,-1,235,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(3/2), x)","F"
624,0,-1,215,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(3/2)), x)","F"
625,0,-1,220,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(3/2)), x)","F"
626,0,-1,371,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{5/2}\,{\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))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(3/2)), x)","F"
627,0,-1,487,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\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))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(3/2)), x)","F"
628,0,-1,588,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(5/2), x)","F"
629,0,-1,472,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(5/2), x)","F"
630,0,-1,368,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B/cos(c + d*x)))/(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)}\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)))/(a + b/cos(c + d*x))^(5/2), x)","F"
631,0,-1,346,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{\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))/(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"
632,0,-1,329,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"
633,0,-1,399,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(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)}}{{\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))/(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"
634,0,-1,526,0.000000,"\text{Not used}","int((A + B/cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{A+\frac{B}{\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}\,{\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))/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2)), x)","F"