1,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
2,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
3,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3), x)","F",0
4,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*cos(d*x + c), x)","F",0
5,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*cos(d*x + c)^2, x)","F",0
6,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
8,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3), x)","F",0
9,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
10,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
11,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(1/3), x)","F",0
12,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(b*sec(d*x + c))^(1/3), x)","F",0
13,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c))^(1/3), x)","F",0
14,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(b*sec(d*x + c))^(1/3), x)","F",0
15,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c))^(1/3), x)","F",0
16,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
17,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
18,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c))^(4/3), x)","F",0
19,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
20,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
21,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^m, x)","F",0
22,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
23,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
24,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
25,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
26,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
27,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
28,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
29,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
30,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n, x)","F",0
31,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
32,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*cos(d*x + c)^2, x)","F",0
33,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*cos(d*x + c)^3, x)","F",0
34,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(5/2), x)","F",0
35,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
36,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
37,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
38,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
39,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
40,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
41,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^2, x)","F",0
42,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c), x)","F",0
43,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3), x)","F",0
44,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c), x)","F",0
45,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c)^2, x)","F",0
46,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c)^3, x)","F",0
47,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3), x)","F",0
50,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
51,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
52,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^3, x)","F",0
53,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
54,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
55,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c))^(2/3), x)","F",0
56,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
57,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
58,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c))^(2/3), x)","F",0
59,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
60,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
61,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c))^(4/3), x)","F",0
62,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
63,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
64,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^3/(b*sec(d*x + c))^(4/3), x)","F",0
65,-1,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
67,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
68,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
69,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
70,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{m}}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
71,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
72,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
73,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
74,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n, x)","F",0
75,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c)^2, x)","F",0
77,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c)^3, x)","F",0
78,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
80,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
81,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
82,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
83,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(5/2), x)","F",0
84,1,175,0,0.334737," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a - 15 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a - 15*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
85,1,152,0,0.338262," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a*tan(d*x + c))/d","A",0
86,1,100,0,0.329121," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, A a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*A*a*log(sec(d*x + c) + tan(d*x + c)) + 12*A*a*tan(d*x + c))/d","A",0
87,1,88,0,0.330122," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a - C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, C a \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a - C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*A*a*log(sec(d*x + c) + tan(d*x + c)) + 4*C*a*tan(d*x + c))/d","A",0
88,1,59,0,0.330345," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} A a + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a \sin\left(d x + c\right) + 2 \, C a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a*sin(d*x + c) + 2*C*a*tan(d*x + c))/d","A",0
89,1,70,0,0.329246," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 4 \, {\left(d x + c\right)} C a + 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a + 4*(d*x + c)*C*a + 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a*sin(d*x + c))/d","A",0
90,1,67,0,0.326634," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 12 \, {\left(d x + c\right)} C a - 12 \, C a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 12*(d*x + c)*C*a - 12*C*a*sin(d*x + c))/d","A",0
91,1,90,0,0.346519," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 96 \, C a \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 96*C*a*sin(d*x + c))/d","A",0
92,1,113,0,0.337345," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a)/d","A",0
93,1,218,0,0.346001," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 8 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 15 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, A a^{2} \tan\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(40*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 8*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 15*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*A*a^2*tan(d*x + c))/d","A",0
94,1,227,0,0.339992," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 96 \, A a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 96*A*a^2*tan(d*x + c))/d","A",0
95,1,131,0,0.356143," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} A a^{2} + 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 6 \, A a^{2} \tan\left(d x + c\right) + 6 \, C a^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A*a^2 + 2*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 6*A*a^2*tan(d*x + c) + 6*C*a^2*tan(d*x + c))/d","A",0
96,1,142,0,0.357857," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} A a^{2} - C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a^{2} \sin\left(d x + c\right) + 8 \, C a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*A*a^2 - C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a^2*sin(d*x + c) + 8*C*a^2*tan(d*x + c))/d","A",0
97,1,101,0,0.349548," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 4 \, {\left(d x + c\right)} A a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 4 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, A a^{2} \sin\left(d x + c\right) + 4 \, C a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 4*(d*x + c)*A*a^2 + 4*(d*x + c)*C*a^2 + 4*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*A*a^2*sin(d*x + c) + 4*C*a^2*tan(d*x + c))/d","A",0
98,1,114,0,0.351500," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 12 \, {\left(d x + c\right)} C a^{2} - 3 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, A a^{2} \sin\left(d x + c\right) - 6 \, C a^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 12*(d*x + c)*C*a^2 - 3*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*A*a^2*sin(d*x + c) - 6*C*a^2*sin(d*x + c))/d","A",0
99,1,132,0,0.342618," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 96 \, {\left(d x + c\right)} C a^{2} - 192 \, C a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(64*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 96*(d*x + c)*C*a^2 - 192*C*a^2*sin(d*x + c))/d","A",0
100,1,156,0,0.362437," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 240 \, C a^{2} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2 - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 240*C*a^2*sin(d*x + c))/d","A",0
101,1,204,0,0.355231," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{128 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2}}{960 \, d}"," ",0,"1/960*(128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2)/d","A",0
102,1,382,0,0.355585," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{3} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 5 \, C a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(480*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^3 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 5*C*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 360*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^3*tan(d*x + c))/d","B",0
103,1,285,0,0.353611," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 45 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 720 \, A a^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 45*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 720*A*a^3*tan(d*x + c))/d","A",0
104,1,250,0,0.355423," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} A a^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, A a^{3} \tan\left(d x + c\right) + 16 \, C a^{3} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(d*x + c)*A*a^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 4*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 48*A*a^3*tan(d*x + c) + 16*C*a^3*tan(d*x + c))/d","A",0
105,1,177,0,0.354847," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{36 \, {\left(d x + c\right)} A a^{3} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 9 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right) + 36 \, C a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(36*(d*x + c)*A*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 9*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 18*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c) + 36*C*a^3*tan(d*x + c))/d","A",0
106,1,175,0,0.352343," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 12 \, {\left(d x + c\right)} A a^{3} + 4 \, {\left(d x + c\right)} C a^{3} - C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 12 \, C a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 12*(d*x + c)*A*a^3 + 4*(d*x + c)*C*a^3 - C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 12*C*a^3*tan(d*x + c))/d","A",0
107,1,137,0,0.351496," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 12 \, {\left(d x + c\right)} A a^{3} - 36 \, {\left(d x + c\right)} C a^{3} - 18 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, A a^{3} \sin\left(d x + c\right) - 12 \, C a^{3} \sin\left(d x + c\right) - 12 \, C a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 12*(d*x + c)*A*a^3 - 36*(d*x + c)*C*a^3 - 18*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*A*a^3*sin(d*x + c) - 12*C*a^3*sin(d*x + c) - 12*C*a^3*tan(d*x + c))/d","A",0
108,1,171,0,0.345517," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 8 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 96 \, {\left(d x + c\right)} C a^{3} - 16 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 32 \, A a^{3} \sin\left(d x + c\right) - 96 \, C a^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"-1/32*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 8*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 96*(d*x + c)*C*a^3 - 16*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 32*A*a^3*sin(d*x + c) - 96*C*a^3*sin(d*x + c))/d","A",0
109,1,190,0,0.346820," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 480 \, {\left(d x + c\right)} C a^{3} + 1440 \, C a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 480*(d*x + c)*C*a^3 + 1440*C*a^3*sin(d*x + c))/d","A",0
110,1,239,0,0.354434," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 960 \, C a^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 960*C*a^3*sin(d*x + c))/d","A",0
111,1,462,0,0.367357," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{56 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{4} + 1680 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 24 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} C a^{4} + 336 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 280 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 35 \, C a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 840 \, A a^{4} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(56*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^4 + 1680*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 24*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*C*a^4 + 336*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 280*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 35*C*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 210*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 210*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 840*A*a^4*tan(d*x + c))/d","B",0
112,1,449,0,0.358502," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 128 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 5 \, C a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 720 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 1920 \, A a^{4} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 5*C*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 720*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 1920*A*a^4*tan(d*x + c))/d","B",0
113,1,308,0,0.350822," ","integrate((a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{20 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 60 \, {\left(d x + c\right)} A a^{4} + 4 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 15 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 360 \, A a^{4} \tan\left(d x + c\right) + 60 \, C a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(20*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 60*(d*x + c)*A*a^4 + 4*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 15*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 360*A*a^4*tan(d*x + c) + 60*C*a^4*tan(d*x + c))/d","A",0
114,1,296,0,0.353484," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{192 \, {\left(d x + c\right)} A a^{4} + 64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 3 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{4} \sin\left(d x + c\right) + 192 \, A a^{4} \tan\left(d x + c\right) + 192 \, C a^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(192*(d*x + c)*A*a^4 + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 3*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 72*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 144*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^4*sin(d*x + c) + 192*A*a^4*tan(d*x + c) + 192*C*a^4*tan(d*x + c))/d","A",0
115,1,211,0,0.352763," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 72 \, {\left(d x + c\right)} A a^{4} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 12 \, {\left(d x + c\right)} C a^{4} - 12 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{4} \sin\left(d x + c\right) + 12 \, A a^{4} \tan\left(d x + c\right) + 72 \, C a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 72*(d*x + c)*A*a^4 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 12*(d*x + c)*C*a^4 - 12*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^4*sin(d*x + c) + 12*A*a^4*tan(d*x + c) + 72*C*a^4*tan(d*x + c))/d","A",0
116,1,211,0,0.363715," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 48 \, {\left(d x + c\right)} A a^{4} - 48 \, {\left(d x + c\right)} C a^{4} + 3 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, A a^{4} \sin\left(d x + c\right) - 12 \, C a^{4} \sin\left(d x + c\right) - 48 \, C a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 48*(d*x + c)*A*a^4 - 48*(d*x + c)*C*a^4 + 3*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 6*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 72*A*a^4*sin(d*x + c) - 12*C*a^4*sin(d*x + c) - 48*C*a^4*tan(d*x + c))/d","A",0
117,1,194,0,0.365477," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 96 \, {\left(d x + c\right)} A a^{4} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 576 \, {\left(d x + c\right)} C a^{4} - 192 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 384 \, A a^{4} \sin\left(d x + c\right) - 384 \, C a^{4} \sin\left(d x + c\right) - 96 \, C a^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(128*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 96*(d*x + c)*A*a^4 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 576*(d*x + c)*C*a^4 - 192*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 384*A*a^4*sin(d*x + c) - 384*C*a^4*sin(d*x + c) - 96*C*a^4*tan(d*x + c))/d","A",0
118,1,229,0,0.365761," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 40 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 480 \, {\left(d x + c\right)} C a^{4} + 60 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, A a^{4} \sin\left(d x + c\right) + 720 \, C a^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 40*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 480*(d*x + c)*C*a^4 + 60*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 120*A*a^4*sin(d*x + c) + 720*C*a^4*sin(d*x + c))/d","A",0
119,1,273,0,0.431944," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{256 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 180 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 960 \, {\left(d x + c\right)} C a^{4} + 3840 \, C a^{4} \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 + 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 960*(d*x + c)*C*a^4 + 3840*C*a^4*sin(d*x + c))/d","A",0
120,1,319,0,0.435777," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{48 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} A a^{4} - 672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 560 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 112 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} + 3360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 1680 \, C a^{4} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"-1/1680*(48*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*A*a^4 - 672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 + 560*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 112*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 3360*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 1680*C*a^4*sin(d*x + c))/d","A",0
121,1,408,0,0.446872," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, {\left(\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a - \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{45 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{24 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 12 \, A {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{24 \, d}"," ",0,"-1/24*(C*(2*(21*sin(d*x + c)/(cos(d*x + c) + 1) - 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a - 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 45*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 24*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 12*A*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
122,1,325,0,0.346342," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 6 \, A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 6*A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
123,1,239,0,0.340251," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 2 \, A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*(C*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 2*A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
124,1,144,0,0.342871," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{A \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - A*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
125,1,125,0,0.522979," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"(A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
126,1,117,0,0.426477," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{C \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
127,1,184,0,0.487004," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(A*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","A",0
128,1,269,0,0.430962," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{3 \, d}"," ",0,"1/3*(A*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
129,1,351,0,0.441307," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 12 \, C {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{12 \, d}"," ",0,"-1/12*(A*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 12*C*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
130,1,379,0,0.378786," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 - 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 30*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 30*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + A*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
131,1,288,0,0.431520," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + A*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2))/d","B",0
132,1,191,0,0.421182," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(C*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) + A*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
133,1,146,0,0.348749," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - A*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
134,1,119,0,0.533032," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(A*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - C*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
135,1,165,0,0.420673," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(A*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) + C*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
136,1,236,0,0.432535," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(A*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + C*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","A",0
137,1,325,0,0.426562," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(A*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + C*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
138,1,330,0,0.437367," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(C*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","A",0
139,1,233,0,0.328872," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*C*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + A*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
140,1,167,0,0.388538," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{3 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(C*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - 3*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
141,1,134,0,0.329741," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(C*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + A*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
142,1,140,0,0.520600," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - \frac{3 \, C {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(A*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - 3*C*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
143,1,205,0,0.489583," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, A {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*A*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + C*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
144,1,276,0,0.539702," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(A*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + C*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
145,1,365,0,0.537190," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{A {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{1380 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + 3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(A*(20*(33*sin(d*x + c)/(cos(d*x + c) + 1) + 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 51*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3 + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (735*sin(d*x + c)/(cos(d*x + c) + 1) - 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 1380*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 3*C*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
146,1,372,0,0.481780," ","integrate(sec(d*x+c)^5*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, C {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} - \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + 5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*C*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 - 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) + 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4))/d","A",0
147,1,274,0,0.331854," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
148,1,228,0,0.490032," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - \frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - A*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
149,1,175,0,0.337538," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
150,1,175,0,0.331172," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
151,1,201,0,0.416976," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - \frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - C*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
152,1,246,0,0.457919," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
153,1,318,0,0.545575," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, A {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} + \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{5880 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + 5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*A*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 + 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 5880*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4))/d","A",0
154,1,405,0,0.528666," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{560 \, {\left(\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{62 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{39 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} + \frac{3 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{21945 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2065 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{231 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{36960 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"1/840*(A*(560*(27*sin(d*x + c)/(cos(d*x + c) + 1) + 62*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 39*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4 + 3*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (21945*sin(d*x + c)/(cos(d*x + c) + 1) - 2065*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 231*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 36960*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + C*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4))/d","A",0
155,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,1,792,0,0.615266," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A}{4 \, d}"," ",0,"1/4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A/d","B",0
161,1,1207,0,0.753743," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{16 \, C \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A}{16 \, d}"," ",0,"1/16*(16*C*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A)/d","B",0
162,1,2713,0,1.036888," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} A + 24 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*((4*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(3/4)*(cos(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(3*d*x + 3*c) - (cos(3*d*x + 3*c) - 1)*sin(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 6*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*((sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 15*sqrt(a)*(arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) + 1) - arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) - 1) - arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - 1)))*A + 24*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
163,1,7699,0,1.229279," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{48 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C - \frac{{\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(36 \, {\left(\sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 36 \, {\left(\sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 9 \, {\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 36 \, {\left(\sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - {\left(32 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 32 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 8 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(16 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 7 \, \cos\left(4 \, d x + 4 \, c\right) - 9\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 8 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, {\left(64 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 36 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - {\left(9 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(9 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(9 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 10 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - 7 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + {\left(9 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(9 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(9 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 26 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 8 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - {\left(32 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 32 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 8 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(16 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 7 \, \cos\left(4 \, d x + 4 \, c\right) - 9\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 8 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, {\left(64 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 4 \, {\left(9 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(9 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)^{2} - 8 \, \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 9 \, {\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 4 \, {\left(4 \, {\left(9 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + {\left(9 \, \cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} - 6 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(64 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{3} + 20 \, {\left(\sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 5 \, \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(5 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(5 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 10 \, \cos\left(4 \, d x + 4 \, c\right) - 11\right)} \sin\left(4 \, d x + 4 \, c\right) - 64 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + 40 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 10 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 2 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + {\left(16 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 17 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 5 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + 2 \, {\left(32 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 8 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, {\left(4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - \sin\left(4 \, d x + 4 \, c\right)^{2} - 40 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 4 \, \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 5 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 2 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 85 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 5 \, {\left(8 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - {\left(64 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{3} + 5 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(5 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(5 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 18 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 37 \, \cos\left(4 \, d x + 4 \, c\right) - 24\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + {\left(5 \, \cos\left(4 \, d x + 4 \, c\right) - 24\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(5 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(5 \, \cos\left(4 \, d x + 4 \, c\right) - 24\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 14 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 43 \, \cos\left(4 \, d x + 4 \, c\right) - 24\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} - 24 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(10 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 10 \, {\left(\cos\left(4 \, d x + 4 \, c\right) - 4\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 50 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(16 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 21 \, \cos\left(4 \, d x + 4 \, c\right) + 5\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 5 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 48 \, \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + {\left(8 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 5 \, \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 2 \, {\left(128 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(5 \, {\left(\cos\left(4 \, d x + 4 \, c\right) - 4\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 2 \, {\left(5 \, \cos\left(4 \, d x + 4 \, c\right) - 24\right)} \sin\left(4 \, d x + 4 \, c\right) + 21 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) - 5 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 5 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} - 105 \, {\left({\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left(-{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left(-{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + 1\right) + {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A}{4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}}{768 \, d}"," ",0,"1/768*(48*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C - (2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(3/4)*((36*(sin(4*d*x + 4*c)^3 + (cos(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 9*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 9*sin(4*d*x + 4*c)^3 + 36*(sin(4*d*x + 4*c)^3 + (cos(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 9*(2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 2*(cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 36*(sin(4*d*x + 4*c)^3 + (cos(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - (32*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*cos(4*d*x + 4*c)^2 + 2*(16*cos(4*d*x + 4*c)^2 + 16*sin(4*d*x + 4*c)^2 - 7*cos(4*d*x + 4*c) - 9)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 8*sin(4*d*x + 4*c)^2 - 2*(64*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 7*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 9*cos(4*d*x + 4*c))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 36*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) - (9*cos(4*d*x + 4*c)^3 + 4*(9*cos(4*d*x + 4*c)^3 + (9*cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c)^2 - 10*cos(4*d*x + 4*c)^2 - 7*cos(4*d*x + 4*c) + 8)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (9*cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c)^2 + 4*(9*cos(4*d*x + 4*c)^3 + (9*cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c)^2 + 26*cos(4*d*x + 4*c)^2 + 25*cos(4*d*x + 4*c) + 8)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*cos(4*d*x + 4*c)^2 - (32*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*cos(4*d*x + 4*c)^2 + 2*(16*cos(4*d*x + 4*c)^2 + 16*sin(4*d*x + 4*c)^2 - 7*cos(4*d*x + 4*c) - 9)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 8*sin(4*d*x + 4*c)^2 - 2*(64*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 7*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 9*cos(4*d*x + 4*c))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(9*cos(4*d*x + 4*c)^3 + (9*cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c)^2 - 8*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 9*(2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 2*(cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*(9*cos(4*d*x + 4*c) + 8)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (9*cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)))*sqrt(a) - 6*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*((64*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 20*(sin(4*d*x + 4*c)^3 + (cos(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*sin(4*d*x + 4*c) + 8*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 5*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 5*sin(4*d*x + 4*c)^3 + 4*(5*sin(4*d*x + 4*c)^3 + (5*cos(4*d*x + 4*c)^2 + 10*cos(4*d*x + 4*c) - 11)*sin(4*d*x + 4*c) - 64*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 40*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 10*(2*sin(4*d*x + 4*c)^3 + 2*(cos(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*sin(4*d*x + 4*c) + cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (16*cos(4*d*x + 4*c)^2 + 16*sin(4*d*x + 4*c)^2 - 17*cos(4*d*x + 4*c) + 1)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 5*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 2*(32*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*cos(4*d*x + 4*c)^2 + 8*(4*cos(4*d*x + 4*c)^2 - sin(4*d*x + 4*c)^2 - 40*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 5*(cos(4*d*x + 4*c) + 1)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*sin(4*d*x + 4*c)^2 - 85*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 5*(8*cos(4*d*x + 4*c)^2 + 8*sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) - (64*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 5*cos(4*d*x + 4*c)^3 + 4*(5*cos(4*d*x + 4*c)^3 + (5*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 - 18*cos(4*d*x + 4*c)^2 + 8*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 37*cos(4*d*x + 4*c) - 24)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (5*cos(4*d*x + 4*c) - 24)*sin(4*d*x + 4*c)^2 + 4*(5*cos(4*d*x + 4*c)^3 + (5*cos(4*d*x + 4*c) - 24)*sin(4*d*x + 4*c)^2 - 14*cos(4*d*x + 4*c)^2 + 16*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 8*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 43*cos(4*d*x + 4*c) - 24)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - 24*cos(4*d*x + 4*c)^2 + 2*(10*cos(4*d*x + 4*c)^3 + 10*(cos(4*d*x + 4*c) - 4)*sin(4*d*x + 4*c)^2 - 50*cos(4*d*x + 4*c)^2 + (16*cos(4*d*x + 4*c)^2 + 16*sin(4*d*x + 4*c)^2 - 21*cos(4*d*x + 4*c) + 5)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 5*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 48*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + (8*cos(4*d*x + 4*c)^2 + 8*sin(4*d*x + 4*c)^2 - 5*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(128*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2*sin(4*d*x + 4*c) + 8*(5*(cos(4*d*x + 4*c) - 4)*sin(4*d*x + 4*c) + 8*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(5*cos(4*d*x + 4*c) - 24)*sin(4*d*x + 4*c) + 21*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 5*(cos(4*d*x + 4*c) + 1)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 5*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)))*sqrt(a) - 105*((4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + cos(4*d*x + 4*c)^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c)^2 - 4*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arctan2(-(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*(cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))) + 1) - (4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + cos(4*d*x + 4*c)^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c)^2 - 4*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arctan2(-(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*(cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1))) - 1) - (4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + cos(4*d*x + 4*c)^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c)^2 - 4*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arctan2((cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + 1) + (4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + cos(4*d*x + 4*c)^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c)^2 - 4*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*arctan2((cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)), (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) - 1))*sqrt(a))*A/(4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + cos(4*d*x + 4*c)^2 + 4*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sin(4*d*x + 4*c)^2 - 4*(4*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))))/d","B",0
164,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,1,804,0,0.598148," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A}{4 \, d}"," ",0,"1/4*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A/d","B",0
169,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,1,1384,0,0.635007," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(18 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(4 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + 5 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(4 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} \cos\left(d x + c\right) + 5 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left({\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \cos\left(d x + c\right) + {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 5 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/4*(18*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((4*a^2*sin(3*d*x + 3*c) + 5*a^2*sin(2*d*x + 2*c) + 4*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*cos(2*d*x + 2*c)^2*sin(d*x + c) + a^2*sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*a^2*cos(2*d*x + 2*c)*sin(d*x + c) + a^2*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (4*a^2*cos(3*d*x + 3*c) + 5*a^2*cos(2*d*x + 2*c) + 4*a^2*cos(d*x + c) + 5*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c)^2 + a^2*cos(d*x + c) + (a^2*cos(d*x + c) - a^2)*sin(2*d*x + 2*c)^2 - a^2 + 2*(a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 5*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","B",0
178,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
185,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
186,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
187,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
188,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
189,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
190,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
191,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
192,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
195,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
196,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
197,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
198,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
199,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
200,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
205,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
206,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
207,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
213,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
214,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
216,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
217,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
218,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
220,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
225,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
226,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
235,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
236,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
237,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
240,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
249,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,1,4417,0,1.160686," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + (420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(15/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(13/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(15/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(13/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
251,1,2740,0,0.896063," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + (60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
252,1,1507,0,0.787277," ","integrate(sec(d*x+c)^(1/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{8 \, A \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} - \frac{{\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{16 \, d}"," ",0,"1/16*(8*A*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)) - (12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
253,1,684,0,0.695010," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) - (4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
254,1,355,0,0.661136," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 3 \, C \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)}}{6 \, d}"," ",0,"1/6*(sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) + 3*C*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)))/d","B",0
255,1,224,0,0.657880," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 120 \, \sqrt{2} C \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, d}"," ",0,"1/60*(sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 120*sqrt(2)*C*sqrt(a)*sin(1/2*d*x + 1/2*c))/d","B",0
256,1,408,0,0.692634," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(105 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 35 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 105 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 35 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 7 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 10 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 140 \, \sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(3*sqrt(2)*(105*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 35*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 7*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 105*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 35*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 7*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 10*sin(7/2*d*x + 7/2*c) + 7*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 140*sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a))/d","B",0
257,1,587,0,0.707267," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(1890 \, \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 420 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 252 \, \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 1890 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 420 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 252 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 45 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 252 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 420 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1890 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 84 \, \sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(1890*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 420*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 252*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 45*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 1890*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 420*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 252*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 45*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*sin(9/2*d*x + 9/2*c) + 45*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 252*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 420*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1890*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) + 84*sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*C*sqrt(a))/d","B",0
258,1,7235,0,1.862190," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{80 \, {\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(7980 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2660 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 38304 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12160 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 45400 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 45400 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12160 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 38304 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2660 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 7980 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7980 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2660 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 38304 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12160 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 45400 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 45400 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12160 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 38304 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2660 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7980 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(5 \, \cos\left(8 \, d x + 8 \, c\right) + 10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + \cos\left(10 \, d x + 10 \, c\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 25 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 100 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 100 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + \sin\left(10 \, d x + 10 \, c\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 25 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 100 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{7680 \, d}"," ",0,"-1/7680*(80*(132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + (7980*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2660*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 38304*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12160*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 45400*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 45400*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12160*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 38304*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2660*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 7980*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7980*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2660*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 38304*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12160*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 45400*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 45400*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12160*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 38304*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2660*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7980*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(5*cos(8*d*x + 8*c) + 10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + cos(10*d*x + 10*c)^2 + 10*(10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 25*cos(8*d*x + 8*c)^2 + 20*(10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 100*cos(6*d*x + 6*c)^2 + 20*(5*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 100*cos(4*d*x + 4*c)^2 + 25*cos(2*d*x + 2*c)^2 + 10*(sin(8*d*x + 8*c) + 2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + sin(10*d*x + 10*c)^2 + 50*(2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 25*sin(8*d*x + 8*c)^2 + 100*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 100*sin(6*d*x + 6*c)^2 + 100*sin(4*d*x + 4*c)^2 + 100*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*sin(2*d*x + 2*c)^2 + 10*cos(2*d*x + 2*c) + 1))/d","B",0
259,1,5761,0,1.276420," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{16 \, {\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1} + \frac{{\left(300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{256 \, d}"," ",0,"-1/256*(16*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
260,1,3506,0,0.967658," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"1/96*(24*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
261,1,2520,0,0.862814," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} - \frac{{\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1}}{16 \, d}"," ",0,"1/16*(4*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) - (56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1))/d","B",0
262,1,1183,0,0.679855," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + \frac{3 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(4*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 3*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
263,1,485,0,0.715274," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 5 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{20 \, d}"," ",0,"1/20*(sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 5*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","B",0
264,1,342,0,0.679638," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 280 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 280*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","B",0
265,1,607,0,0.717205," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3780 \, a \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1050 \, a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 378 \, a \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 3780 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 1050 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 378 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 135 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 378 \, a \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1050 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 3780 \, a \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 252 \, \sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(3780*a*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 1050*a*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 378*a*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 135*a*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 3780*a*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 1050*a*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 378*a*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 135*a*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a*sin(9/2*d*x + 9/2*c) + 135*a*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 378*a*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1050*a*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 3780*a*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) + 252*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*C*sqrt(a))/d","B",0
266,1,794,0,0.744816," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{7 \, \sqrt{2} {\left(3630 \, a \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 990 \, a \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 429 \, a \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 165 \, a \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 3630 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 990 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 429 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 165 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 55 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 165 \, a \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 429 \, a \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 990 \, a \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3630 \, a \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 44 \, \sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{36960 \, d}"," ",0,"1/36960*(7*sqrt(2)*(3630*a*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 990*a*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 429*a*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 165*a*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 55*a*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 3630*a*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 990*a*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 429*a*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 165*a*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 55*a*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 30*a*sin(11/2*d*x + 11/2*c) + 55*a*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 165*a*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 429*a*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 990*a*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3630*a*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) + 44*sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*C*sqrt(a))/d","B",0
267,1,11081,0,3.249768," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(12180 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{23}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4060 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{21}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 70644 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 22620 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 147592 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 37800 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 37800 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 147592 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 22620 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 70644 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4060 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12180 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 12180 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{23}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4060 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{21}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 70644 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 22620 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 147592 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 37800 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 37800 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 147592 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 22620 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 70644 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4060 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12180 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(6 \, \cos\left(10 \, d x + 10 \, c\right) + 15 \, \cos\left(8 \, d x + 8 \, c\right) + 20 \, \cos\left(6 \, d x + 6 \, c\right) + 15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(12 \, d x + 12 \, c\right) + \cos\left(12 \, d x + 12 \, c\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, d x + 8 \, c\right) + 20 \, \cos\left(6 \, d x + 6 \, c\right) + 15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + 36 \, \cos\left(10 \, d x + 10 \, c\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, d x + 6 \, c\right) + 15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 225 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 400 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 225 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + \sin\left(12 \, d x + 12 \, c\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 36 \, \sin\left(10 \, d x + 10 \, c\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 225 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 400 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{6144 \, d}"," ",0,"-1/6144*(8*(1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1) + (12180*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(23/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4060*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(21/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 70644*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 22620*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 147592*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 37800*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 37800*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 147592*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 22620*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 70644*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4060*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12180*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 12180*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(23/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4060*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(21/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 70644*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 22620*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 147592*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 37800*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 37800*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 147592*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 22620*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 70644*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4060*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12180*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(6*cos(10*d*x + 10*c) + 15*cos(8*d*x + 8*c) + 20*cos(6*d*x + 6*c) + 15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(12*d*x + 12*c) + cos(12*d*x + 12*c)^2 + 12*(15*cos(8*d*x + 8*c) + 20*cos(6*d*x + 6*c) + 15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + 36*cos(10*d*x + 10*c)^2 + 30*(20*cos(6*d*x + 6*c) + 15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 225*cos(8*d*x + 8*c)^2 + 40*(15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 400*cos(6*d*x + 6*c)^2 + 30*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 225*cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 2*(6*sin(10*d*x + 10*c) + 15*sin(8*d*x + 8*c) + 20*sin(6*d*x + 6*c) + 15*sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + sin(12*d*x + 12*c)^2 + 12*(15*sin(8*d*x + 8*c) + 20*sin(6*d*x + 6*c) + 15*sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 36*sin(10*d*x + 10*c)^2 + 30*(20*sin(6*d*x + 6*c) + 15*sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 225*sin(8*d*x + 8*c)^2 + 120*(5*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 400*sin(6*d*x + 6*c)^2 + 225*sin(4*d*x + 4*c)^2 + 180*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 12*cos(2*d*x + 2*c) + 1))/d","B",0
268,1,8852,0,2.048325," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{80 \, {\left(300 \, \sqrt{2} a^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(6 \, d x + 6 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 28 \, {\left(\sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 300 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{11}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(7 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 114 \, \sqrt{2} a^{2} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 114 \, \sqrt{2} a^{2} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 456 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 456 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(7 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 28 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 300 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 114 \, \sqrt{2} a^{2} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 114 \, \sqrt{2} a^{2} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 75 \, \sqrt{2} a^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 456 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 456 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 75 \, \sqrt{2} a^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 300 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{\cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 3 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(6 \, d x + 6 \, c\right) + 1} - \frac{{\left(16980 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 5660 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 81504 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8320 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 86440 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 86440 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8320 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 81504 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 5660 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16980 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16980 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 5660 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 81504 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8320 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 86440 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 86440 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8320 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 81504 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 5660 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16980 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(5 \, \cos\left(8 \, d x + 8 \, c\right) + 10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + \cos\left(10 \, d x + 10 \, c\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 25 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 100 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 100 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + \sin\left(10 \, d x + 10 \, c\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 25 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 100 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{7680 \, d}"," ",0,"1/7680*(80*(300*sqrt(2)*a^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(6*d*x + 6*c) - 28*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 28*(sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) - sqrt(2)*a^2*sin(3/2*d*x + 3/2*c))*cos(6*d*x + 6*c) - 300*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 3*sqrt(2)*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(11/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(7*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 114*sqrt(2)*a^2*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 114*sqrt(2)*a^2*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 75*sqrt(2)*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 456*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 456*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(7*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 75*sqrt(2)*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 28*(sqrt(2)*a^2*cos(9/2*d*x + 9/2*c) - sqrt(2)*a^2*cos(3/2*d*x + 3/2*c))*sin(6*d*x + 6*c) + 300*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 3*sqrt(2)*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*sin(11/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(7*sqrt(2)*a^2*cos(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 114*sqrt(2)*a^2*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 114*sqrt(2)*a^2*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 75*sqrt(2)*a^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 456*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 3*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 456*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 3*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(7*sqrt(2)*a^2*cos(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 75*sqrt(2)*a^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 300*(sqrt(2)*a^2*cos(6*d*x + 6*c) + sqrt(2)*a^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(cos(6*d*x + 6*c)^2 + 6*(cos(6*d*x + 6*c) + 3*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*(cos(6*d*x + 6*c) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(6*d*x + 6*c)^2 + 6*(sin(6*d*x + 6*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(6*d*x + 6*c) + 1) - (16980*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 5660*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 81504*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8320*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 86440*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 86440*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8320*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 81504*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 5660*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16980*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16980*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 5660*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 81504*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8320*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 86440*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 86440*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8320*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 81504*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 5660*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16980*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(5*cos(8*d*x + 8*c) + 10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + cos(10*d*x + 10*c)^2 + 10*(10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 25*cos(8*d*x + 8*c)^2 + 20*(10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 100*cos(6*d*x + 6*c)^2 + 20*(5*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 100*cos(4*d*x + 4*c)^2 + 25*cos(2*d*x + 2*c)^2 + 10*(sin(8*d*x + 8*c) + 2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + sin(10*d*x + 10*c)^2 + 50*(2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 25*sin(8*d*x + 8*c)^2 + 100*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 100*sin(6*d*x + 6*c)^2 + 100*sin(4*d*x + 4*c)^2 + 100*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*sin(2*d*x + 2*c)^2 + 10*cos(2*d*x + 2*c) + 1))/d","B",0
269,1,6687,0,4.741793," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(88 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 56 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 44 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(22 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 14 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 38 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(11 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 44 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 28 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(88*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 56*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 44*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 2*(22*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) - 14*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 38*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 4*(11*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c) - 7*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c) + 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 44*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) + 28*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c) + 8*(7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + (1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
270,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,1,3421,0,4.417436," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(30 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 30 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - \frac{3 \, {\left(88 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 56 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 44 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(22 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 14 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 38 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(11 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 44 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 28 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{48 \, d}"," ",0,"1/48*(4*sqrt(2)*(30*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 30*a^2*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*a^2*sin(3/2*d*x + 3/2*c) + 30*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) - 3*(88*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 56*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 44*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 2*(22*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) - 14*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 38*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 4*(11*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c) - 7*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c) + 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 44*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) + 28*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c) + 8*(7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
272,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,1,917,0,0.910022," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 14 \, \sqrt{2} {\left(30 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 30 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{168 \, d}"," ",0,"1/168*(sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 14*sqrt(2)*(30*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 30*a^2*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*a^2*sin(3/2*d*x + 3/2*c) + 30*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a))/d","B",0
274,1,483,0,0.782146," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 168 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) + 168*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","B",0
275,1,845,0,0.708415," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(31878 \, a^{2} \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 8778 \, a^{2} \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 3465 \, a^{2} \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1287 \, a^{2} \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 31878 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 8778 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 3465 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1287 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 385 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 126 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1287 \, a^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3465 \, a^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 8778 \, a^{2} \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 31878 \, a^{2} \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 132 \, \sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{22176 \, d}"," ",0,"1/22176*(sqrt(2)*(31878*a^2*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 8778*a^2*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 3465*a^2*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 1287*a^2*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 385*a^2*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 31878*a^2*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 8778*a^2*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 3465*a^2*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1287*a^2*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 385*a^2*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 126*a^2*sin(11/2*d*x + 11/2*c) + 385*a^2*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1287*a^2*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3465*a^2*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 8778*a^2*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 31878*a^2*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) + 132*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*C*sqrt(a))/d","B",0
276,1,1043,0,0.933303," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3783780 \, a^{2} \cos\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 1066065 \, a^{2} \cos\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 459459 \, a^{2} \cos\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 193050 \, a^{2} \cos\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 70070 \, a^{2} \cos\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \cos\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 3783780 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 1066065 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 459459 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 193050 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 70070 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 20475 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 6930 \, a^{2} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \sin\left(\frac{11}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 70070 \, a^{2} \sin\left(\frac{9}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 193050 \, a^{2} \sin\left(\frac{7}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 459459 \, a^{2} \sin\left(\frac{5}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 1066065 \, a^{2} \sin\left(\frac{3}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 3783780 \, a^{2} \sin\left(\frac{1}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 572 \, \sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{2882880 \, d}"," ",0,"1/2882880*(sqrt(2)*(3783780*a^2*cos(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 1066065*a^2*cos(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 459459*a^2*cos(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 193050*a^2*cos(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 70070*a^2*cos(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 20475*a^2*cos(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) - 3783780*a^2*cos(13/2*d*x + 13/2*c)*sin(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 1066065*a^2*cos(13/2*d*x + 13/2*c)*sin(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 459459*a^2*cos(13/2*d*x + 13/2*c)*sin(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 193050*a^2*cos(13/2*d*x + 13/2*c)*sin(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 70070*a^2*cos(13/2*d*x + 13/2*c)*sin(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 20475*a^2*cos(13/2*d*x + 13/2*c)*sin(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 6930*a^2*sin(13/2*d*x + 13/2*c) + 20475*a^2*sin(11/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 70070*a^2*sin(9/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 193050*a^2*sin(7/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 459459*a^2*sin(5/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 1066065*a^2*sin(3/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 3783780*a^2*sin(1/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))))*A*sqrt(a) + 572*sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*C*sqrt(a))/d","B",0
277,1,3562,0,1.033820," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} + \frac{{\left(84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C}{{\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)) + (84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
278,1,2124,0,0.962278," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} A}{\sqrt{a}} - \frac{{\left(4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{16 \, d}"," ",0,"-1/16*(8*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*A/sqrt(a) - (4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
279,1,968,0,0.867243," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} A}{\sqrt{a}} - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*(2*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*A/sqrt(a) - (4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
280,1,580,0,0.725023," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{\sqrt{a}} + \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} C}{\sqrt{a}}}{2 \, d}"," ",0,"-1/2*((sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*A/sqrt(a) + (sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*C/sqrt(a))/d","B",0
281,1,373,0,0.715585," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{3 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} C}{\sqrt{a}}}{6 \, d}"," ",0,"-1/6*((3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A/sqrt(a) - 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*C/sqrt(a))/d","B",0
282,1,462,0,0.731229," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{2} {\left(60 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 60 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 60 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{30 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C}{\sqrt{a}}}{60 \, d}"," ",0,"1/60*(sqrt(2)*(60*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 60*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 6*sin(5/2*d*x + 5/2*c) - 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 60*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A/sqrt(a) - 30*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*C/sqrt(a))/d","B",0
283,1,730,0,0.779622," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{2} {\left(525 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 175 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 525 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) + 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) - 30 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 525 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} + \frac{140 \, {\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C}{\sqrt{a}}}{840 \, d}"," ",0,"-1/840*(sqrt(2)*(525*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 175*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 525*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) + 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 - 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) - 30*sin(7/2*d*x + 7/2*c) + 21*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 525*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A/sqrt(a) + 140*(3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C/sqrt(a))/d","B",0
284,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,1,3153,0,0.893967," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 12 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(d x + c\right) + 4 \, {\left(3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(d x + c\right) - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(d x + c\right) + 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 4 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{{\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(d x + c\right)^{2} + \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 4 \, \sqrt{2} a \sin\left(d x + c\right)^{2} + 4 \, \sqrt{2} a \cos\left(d x + c\right) + 2 \, {\left(2 \, \sqrt{2} a \cos\left(d x + c\right) + \sqrt{2} a\right)} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sqrt{a}} + \frac{{\left(4 \, {\left(\sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 5 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 5 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*((3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 + 2*(6*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 2*sin(3/2*d*x + 3/2*c) + 2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 4*(3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 4*(3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + cos(3/2*d*x + 3/2*c) - cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*(2*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 8*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 8*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 4*sin(1/2*d*x + 1/2*c))*A/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 4*sqrt(2)*a*sin(d*x + c)^2 + 4*sqrt(2)*a*cos(d*x + c) + 2*(2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*sqrt(a)) + (4*(sin(2*d*x + 2*c) + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 5*(cos(2*d*x + 2*c)^2 + 4*(cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(2*d*x + 2*c)^2 + 4*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 5*(cos(2*d*x + 2*c)^2 + 4*(cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(2*d*x + 2*c)^2 + 4*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 4*(cos(2*d*x + 2*c) + 2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 4*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*sqrt(a)))/d","B",0
286,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
289,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,1,7863,0,1.372581," ","integrate(sec(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 40 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 24 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 24 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, {\left(16 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 48 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 5 \, {\left(16 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 48 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 48 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(3 \, d x + 3 \, c\right) + 80 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(3 \, d x + 3 \, c\right) + 48 \, \cos\left(3 \, d x + 3 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 20 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 20 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} A}{{\left(16 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + \sqrt{2} a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 36 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 48 \, {\left(\sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a}} + \frac{{\left(44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(19 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(19 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 176 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 176 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a}}}{32 \, d}"," ",0,"1/32*((4*(3*sin(3/2*d*x + 3/2*c) + 5*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 40*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 24*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 24*(3*sin(3/2*d*x + 3/2*c) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*(3*sin(3/2*d*x + 3/2*c) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*(16*cos(3*d*x + 3*c)^2 + 2*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(4*cos(3*d*x + 3*c) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(4*cos(3*d*x + 3*c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sin(3*d*x + 3*c)^2 + 4*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 48*(sin(3*d*x + 3*c) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*cos(3*d*x + 3*c) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 5*(16*cos(3*d*x + 3*c)^2 + 2*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(4*cos(3*d*x + 3*c) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(4*cos(3*d*x + 3*c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sin(3*d*x + 3*c)^2 + 4*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 48*(sin(3*d*x + 3*c) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*cos(3*d*x + 3*c) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 48*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 80*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + 48*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*(3*cos(3/2*d*x + 3/2*c) + 5*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*(3*cos(3/2*d*x + 3/2*c) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*(3*cos(3/2*d*x + 3/2*c) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(4*cos(3*d*x + 3*c) + 1)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*sin(3/2*d*x + 3/2*c))*A/((16*sqrt(2)*a^2*cos(3*d*x + 3*c)^2 + sqrt(2)*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 36*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sqrt(2)*a^2*sin(3*d*x + 3*c)^2 + sqrt(2)*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 36*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sqrt(2)*a^2*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*sqrt(2)*a^2*cos(3*d*x + 3*c) + sqrt(2)*a^2 + 2*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 6*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 4*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + sqrt(2)*a^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(2*sqrt(2)*a^2*sin(3*d*x + 3*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 48*(sqrt(2)*a^2*sin(3*d*x + 3*c) + sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)) + (44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(19*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(19*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 176*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 176*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2 + 2*(6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(4*d*x + 4*c) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c) + 4*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)))/d","B",0
291,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
296,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
297,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(4/3), x)","F",0
298,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(7/3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(4/3), x)","F",0
300,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^(1/3), x)","F",0
301,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(2/3), x)","F",0
302,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
303,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^m, x)","F",0
304,0,0,0,0.000000," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
305,1,310,0,4.818946," ","integrate((a+a*sec(d*x+c))^n*(-a*A*n-a*C*(1+n)*sec(d*x+c))/a/(1+n)/(sec(d*x+c)^n)+sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(-{\left(d n + d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - c\right) \sin\left(c n\right) - {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(-{\left(d n - d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + c\right) \sin\left(c n\right) - {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(c n\right) \sin\left(-{\left(d n + d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - c\right) + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(c n\right) \sin\left(-{\left(d n - d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + c\right)}{2 \, {\left({\left(d n + d\right)} 2^{n} \cos\left(c n\right)^{2} + {\left(d n + d\right)} 2^{n} \sin\left(c n\right)^{2}\right)}}"," ",0,"1/2*((cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(-(d*n + d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) - c)*sin(c*n) - (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(-(d*n - d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) + c)*sin(c*n) - (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(c*n)*sin(-(d*n + d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) - c) + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(c*n)*sin(-(d*n - d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) + c))/((d*n + d)*2^n*cos(c*n)^2 + (d*n + d)*2^n*sin(c*n)^2)","B",0
306,1,163,0,0.474883," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
307,1,127,0,0.422668," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*B*a*tan(d*x + c))/d","A",0
308,1,88,0,0.429719," ","integrate((a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, B a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 4 \, B a \tan\left(d x + c\right) - 4 \, C a \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*B*a*log(sec(d*x + c) + tan(d*x + c)) - 4*B*a*tan(d*x + c) - 4*C*a*tan(d*x + c))/d","A",0
309,1,73,0,0.377422," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a*tan(d*x + c))/d","B",0
310,1,58,0,0.346460," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + 2 \, {\left(d x + c\right)} C a + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + 2*(d*x + c)*C*a + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a*sin(d*x + c))/d","A",0
311,1,55,0,0.365705," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a + 4 \, {\left(d x + c\right)} C a + 4 \, B a \sin\left(d x + c\right) + 4 \, C a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a + 4*(d*x + c)*C*a + 4*B*a*sin(d*x + c) + 4*C*a*sin(d*x + c))/d","A",0
312,1,79,0,0.343775," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 12 \, C a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 12*C*a*sin(d*x + c))/d","A",0
313,1,101,0,0.346413," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a)/d","A",0
314,1,278,0,0.478111," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 15 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 15*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
315,1,230,0,0.449275," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 32*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 24*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*B*a^2*tan(d*x + c))/d","A",0
316,1,167,0,0.447089," ","integrate((a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 24 \, B a^{2} \tan\left(d x + c\right) + 12 \, C a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 6*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*B*a^2*log(sec(d*x + c) + tan(d*x + c)) + 24*B*a^2*tan(d*x + c) + 12*C*a^2*tan(d*x + c))/d","A",0
317,1,142,0,0.343179," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{2} - C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} \tan\left(d x + c\right) + 8 \, C a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a^2 - C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^2*tan(d*x + c) + 8*C*a^2*tan(d*x + c))/d","A",0
318,1,105,0,0.417694," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{2} + 2 \, {\left(d x + c\right)} C a^{2} + B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a^{2} \sin\left(d x + c\right) + 2 \, C a^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*B*a^2 + 2*(d*x + c)*C*a^2 + B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a^2*sin(d*x + c) + 2*C*a^2*tan(d*x + c))/d","A",0
319,1,101,0,0.480590," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 4 \, {\left(d x + c\right)} B a^{2} + 8 \, {\left(d x + c\right)} C a^{2} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, B a^{2} \sin\left(d x + c\right) + 4 \, C a^{2} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 + 4*(d*x + c)*B*a^2 + 8*(d*x + c)*C*a^2 + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*B*a^2*sin(d*x + c) + 4*C*a^2*sin(d*x + c))/d","A",0
320,1,110,0,0.387556," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 12 \, {\left(d x + c\right)} C a^{2} - 12 \, B a^{2} \sin\left(d x + c\right) - 24 \, C a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 12*(d*x + c)*C*a^2 - 12*B*a^2*sin(d*x + c) - 24*C*a^2*sin(d*x + c))/d","A",0
321,1,144,0,0.378897," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 96 \, C a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(64*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 96*C*a^2*sin(d*x + c))/d","A",0
322,1,178,0,0.460609," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2}}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2)/d","A",0
323,1,337,0,0.473081," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 15 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 45 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, B a^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 15*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 45*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*B*a^3*tan(d*x + c))/d","B",0
324,1,262,0,0.483877," ","integrate((a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 3 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 144 \, B a^{3} \tan\left(d x + c\right) + 48 \, C a^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 3*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 36*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*B*a^3*log(sec(d*x + c) + tan(d*x + c)) + 144*B*a^3*tan(d*x + c) + 48*C*a^3*tan(d*x + c))/d","B",0
325,1,212,0,0.445984," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{3} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 3 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 9 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{3} \tan\left(d x + c\right) + 36 \, C a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*B*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 3*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 9*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 18*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^3*tan(d*x + c) + 36*C*a^3*tan(d*x + c))/d","B",0
326,1,165,0,0.366021," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{3} + 4 \, {\left(d x + c\right)} C a^{3} - C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{3} \sin\left(d x + c\right) + 4 \, B a^{3} \tan\left(d x + c\right) + 12 \, C a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*B*a^3 + 4*(d*x + c)*C*a^3 - C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^3*sin(d*x + c) + 4*B*a^3*tan(d*x + c) + 12*C*a^3*tan(d*x + c))/d","A",0
327,1,140,0,0.369584," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 12 \, {\left(d x + c\right)} B a^{3} + 12 \, {\left(d x + c\right)} C a^{3} + 2 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{3} \sin\left(d x + c\right) + 4 \, C a^{3} \sin\left(d x + c\right) + 4 \, C a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 12*(d*x + c)*B*a^3 + 12*(d*x + c)*C*a^3 + 2*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*B*a^3*sin(d*x + c) + 4*C*a^3*sin(d*x + c) + 4*C*a^3*tan(d*x + c))/d","A",0
328,1,148,0,0.413370," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 12 \, {\left(d x + c\right)} B a^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 36 \, {\left(d x + c\right)} C a^{3} - 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a^{3} \sin\left(d x + c\right) - 36 \, C a^{3} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 12*(d*x + c)*B*a^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 36*(d*x + c)*C*a^3 - 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*B*a^3*sin(d*x + c) - 36*C*a^3*sin(d*x + c))/d","A",0
329,1,167,0,0.430944," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 96 \, {\left(d x + c\right)} C a^{3} - 96 \, B a^{3} \sin\left(d x + c\right) - 288 \, C a^{3} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(96*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 96*(d*x + c)*C*a^3 - 96*B*a^3*sin(d*x + c) - 288*C*a^3*sin(d*x + c))/d","A",0
330,1,213,0,0.343170," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 480 \, C a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 480*C*a^3*sin(d*x + c))/d","A",0
331,1,262,0,0.359091," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{3} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3}}{960 \, d}"," ",0,"1/960*(192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3)/d","A",0
332,1,368,0,0.349478," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, B {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*B*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
333,1,282,0,0.412099," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 2 \, B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*(C*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 2*B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
334,1,196,0,0.341761," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
335,1,99,0,0.335576," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{B \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
336,1,73,0,0.537288," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{C \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + C*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
337,1,143,0,0.429863," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
338,1,225,0,0.432183," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{B {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(B*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) + C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
339,1,310,0,0.450902," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, C {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{3 \, d}"," ",0,"1/3*(B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*C*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
340,1,336,0,0.339666," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"-1/6*(C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
341,1,244,0,0.353757," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"1/6*(C*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2))/d","B",0
342,1,145,0,0.372602," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
343,1,93,0,0.359899," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(C*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 + B*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
344,1,120,0,0.441995," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(B*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - C*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
345,1,191,0,0.440411," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"1/6*(B*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - C*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
346,1,283,0,0.451140," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"-1/6*(B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - C*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
347,1,372,0,0.551353," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{B {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"1/6*(B*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
348,1,377,0,0.395903," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - 3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(C*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - 3*B*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","A",0
349,1,286,0,0.394389," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(3*C*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","A",0
350,1,187,0,0.447406," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(C*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
351,1,115,0,0.444356," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, B {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(C*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + 3*B*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
352,1,115,0,0.457725," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, C {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(B*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + 3*C*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
353,1,160,0,0.603680," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(B*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - C*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
354,1,231,0,0.545829," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(3*B*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - C*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
355,1,322,0,0.557580," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{B {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - 3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(B*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - 3*C*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
356,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(3 \, B \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(3 \, B \cos\left(2 \, d x + 2 \, c\right) + 3 \, B + 2 \, C\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} - \frac{1}{2} \, \sqrt{a} {\left(\frac{\frac{3}{2} \, {\left({\left(B + 2 \, C\right)} d \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(B + 2 \, C\right)} d \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(B + 2 \, C\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(B + 2 \, C\right)} d\right)} {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} d \int \frac{{\left({\left(\cos\left(6 \, d x + 6 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + {\left(\cos\left(2 \, d x + 2 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left({\left(\cos\left(2 \, d x + 2 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(\cos\left(6 \, d x + 6 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{2 \, {\left({\left(2 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}\,{d x} + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} d} + \frac{\frac{3}{2} \, {\left(B d \cos\left(2 \, d x + 2 \, c\right)^{2} + B d \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, B d \cos\left(2 \, d x + 2 \, c\right) + B d\right)} {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} d \int \frac{{\left({\left(\cos\left(6 \, d x + 6 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + {\left(\cos\left(2 \, d x + 2 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left({\left(\cos\left(2 \, d x + 2 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(\cos\left(6 \, d x + 6 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{2 \, {\left({\left(2 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}\,{d x} - 3 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} d}\right)}\right)}}{3 \, {\left(d \cos\left(2 \, d x + 2 \, c\right)^{2} + d \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x + 2 \, c\right) + d\right)}}"," ",0,"-2/3*((3*B*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(2*d*x + 2*c) - (3*B*cos(2*d*x + 2*c) + 3*B + 2*C)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) - 3*(((B + 2*C)*d*cos(2*d*x + 2*c)^2 + (B + 2*C)*d*sin(2*d*x + 2*c)^2 + 2*(B + 2*C)*d*cos(2*d*x + 2*c) + (B + 2*C)*d)*integrate((((cos(6*d*x + 6*c)*cos(2*d*x + 2*c) + 2*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + sin(6*d*x + 6*c)*sin(2*d*x + 2*c) + 2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + (cos(2*d*x + 2*c)*sin(6*d*x + 6*c) + 2*cos(2*d*x + 2*c)*sin(4*d*x + 4*c) - cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((cos(2*d*x + 2*c)*sin(6*d*x + 6*c) + 2*cos(2*d*x + 2*c)*sin(4*d*x + 4*c) - cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (cos(6*d*x + 6*c)*cos(2*d*x + 2*c) + 2*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + sin(6*d*x + 6*c)*sin(2*d*x + 2*c) + 2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))/(((2*(2*cos(4*d*x + 4*c) + cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 4*cos(4*d*x + 4*c)^2 + 4*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + 2*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 4*sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (2*(2*cos(4*d*x + 4*c) + cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 4*cos(4*d*x + 4*c)^2 + 4*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + 2*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 4*sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)), x) + (B*d*cos(2*d*x + 2*c)^2 + B*d*sin(2*d*x + 2*c)^2 + 2*B*d*cos(2*d*x + 2*c) + B*d)*integrate((((cos(6*d*x + 6*c)*cos(2*d*x + 2*c) + 2*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + sin(6*d*x + 6*c)*sin(2*d*x + 2*c) + 2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + (cos(2*d*x + 2*c)*sin(6*d*x + 6*c) + 2*cos(2*d*x + 2*c)*sin(4*d*x + 4*c) - cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((cos(2*d*x + 2*c)*sin(6*d*x + 6*c) + 2*cos(2*d*x + 2*c)*sin(4*d*x + 4*c) - cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (cos(6*d*x + 6*c)*cos(2*d*x + 2*c) + 2*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + sin(6*d*x + 6*c)*sin(2*d*x + 2*c) + 2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))/(((2*(2*cos(4*d*x + 4*c) + cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 4*cos(4*d*x + 4*c)^2 + 4*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + 2*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 4*sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (2*(2*cos(4*d*x + 4*c) + cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 4*cos(4*d*x + 4*c)^2 + 4*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + 2*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 4*sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)), x))*sqrt(a))/(d*cos(2*d*x + 2*c)^2 + d*sin(2*d*x + 2*c)^2 + 2*d*cos(2*d*x + 2*c) + d)","F",0
361,1,147,0,0.506909," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{B \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right)}{d}"," ",0,"B*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c))/d","B",0
362,1,939,0,0.794138," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{4 \, C \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B}{4 \, d}"," ",0,"1/4*(4*C*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B)/d","B",0
363,1,1851,0,0.987999," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B + 4 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{16 \, d}"," ",0,"1/16*((2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B + 4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
364,1,2981,0,1.207738," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} B + 6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*((4*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(3/4)*(cos(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(3*d*x + 3*c) - (cos(3*d*x + 3*c) - 1)*sin(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 6*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*((sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 15*sqrt(a)*(arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) + 1) - arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) - 1) - arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - 1)))*B + 6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
365,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,1,998,0,0.718733," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} B}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/2*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*B/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
370,1,1801,0,0.882510," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B + \frac{2 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}}{4 \, d}"," ",0,"1/4*((2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B + 2*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/d","B",0
371,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,1,1396,0,0.649814," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B}{6 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/6*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","B",0
379,1,2780,0,0.855701," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(18 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(4 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + 5 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(4 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} \cos\left(d x + c\right) + 5 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left({\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \cos\left(d x + c\right) + {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 5 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{2 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(3*(18*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((4*a^2*sin(3*d*x + 3*c) + 5*a^2*sin(2*d*x + 2*c) + 4*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*cos(2*d*x + 2*c)^2*sin(d*x + c) + a^2*sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*a^2*cos(2*d*x + 2*c)*sin(d*x + c) + a^2*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (4*a^2*cos(3*d*x + 3*c) + 5*a^2*cos(2*d*x + 2*c) + 4*a^2*cos(d*x + c) + 5*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c)^2 + a^2*cos(d*x + c) + (a^2*cos(d*x + c) - a^2)*sin(2*d*x + 2*c)^2 - a^2 + 2*(a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 5*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 2*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
380,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
385,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
386,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
387,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
388,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(a*sec(d*x + c) + a), x)","F",0
389,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
390,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
391,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
392,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
393,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
395,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
397,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(a*sec(d*x + c) + a)^(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
400,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
401,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(a*sec(d*x + c) + a)^(5/2), x)","F",0
406,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
407,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
408,1,266,0,0.380216," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a - 15 \, B a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a - 15*B*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
409,1,218,0,0.367675," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a*tan(d*x + c))/d","A",0
410,1,155,0,0.369211," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, A a \tan\left(d x + c\right) + 12 \, B a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*A*a*log(sec(d*x + c) + tan(d*x + c)) + 12*A*a*tan(d*x + c) + 12*B*a*tan(d*x + c))/d","A",0
411,1,116,0,0.385035," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a - C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, B a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, B a \tan\left(d x + c\right) + 4 \, C a \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a - C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*A*a*log(sec(d*x + c) + tan(d*x + c)) + 4*B*a*log(sec(d*x + c) + tan(d*x + c)) + 4*B*a*tan(d*x + c) + 4*C*a*tan(d*x + c))/d","A",0
412,1,92,0,0.402425," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} A a + 2 \, {\left(d x + c\right)} B a + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a \sin\left(d x + c\right) + 2 \, C a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*a + 2*(d*x + c)*B*a + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a*sin(d*x + c) + 2*C*a*tan(d*x + c))/d","A",0
413,1,89,0,0.364051," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 4 \, {\left(d x + c\right)} B a + 4 \, {\left(d x + c\right)} C a + 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a \sin\left(d x + c\right) + 4 \, B a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a + 4*(d*x + c)*B*a + 4*(d*x + c)*C*a + 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a*sin(d*x + c) + 4*B*a*sin(d*x + c))/d","A",0
414,1,98,0,0.370898," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 12 \, {\left(d x + c\right)} C a - 12 \, B a \sin\left(d x + c\right) - 12 \, C a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 12*(d*x + c)*C*a - 12*B*a*sin(d*x + c) - 12*C*a*sin(d*x + c))/d","A",0
415,1,132,0,0.368240," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 96 \, C a \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 96*C*a*sin(d*x + c))/d","A",0
416,1,166,0,0.368978," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a)/d","A",0
417,1,477,0,0.366072," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 64 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{2} - 5 \, C a^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"1/480*(320*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 64*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^2 - 5*C*a^2*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","B",0
418,1,360,0,0.372458," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 15 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{2} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 15*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^2*tan(d*x + c))/d","B",0
419,1,309,0,0.389822," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 96 \, A a^{2} \tan\left(d x + c\right) + 48 \, B a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 32*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 24*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 96*A*a^2*tan(d*x + c) + 48*B*a^2*tan(d*x + c))/d","B",0
420,1,210,0,0.376273," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a^{2} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, B a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, A a^{2} \tan\left(d x + c\right) + 24 \, B a^{2} \tan\left(d x + c\right) + 12 \, C a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a^2 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 6*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 12*B*a^2*log(sec(d*x + c) + tan(d*x + c)) + 12*A*a^2*tan(d*x + c) + 24*B*a^2*tan(d*x + c) + 12*C*a^2*tan(d*x + c))/d","A",0
421,1,192,0,0.400810," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} A a^{2} + 4 \, {\left(d x + c\right)} B a^{2} - C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a^{2} \sin\left(d x + c\right) + 4 \, B a^{2} \tan\left(d x + c\right) + 8 \, C a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*A*a^2 + 4*(d*x + c)*B*a^2 - C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a^2*sin(d*x + c) + 4*B*a^2*tan(d*x + c) + 8*C*a^2*tan(d*x + c))/d","A",0
422,1,151,0,0.371604," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 4 \, {\left(d x + c\right)} A a^{2} + 8 \, {\left(d x + c\right)} B a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, A a^{2} \sin\left(d x + c\right) + 4 \, B a^{2} \sin\left(d x + c\right) + 4 \, C a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 4*(d*x + c)*A*a^2 + 8*(d*x + c)*B*a^2 + 4*(d*x + c)*C*a^2 + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*A*a^2*sin(d*x + c) + 4*B*a^2*sin(d*x + c) + 4*C*a^2*tan(d*x + c))/d","A",0
423,1,160,0,0.414872," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 12 \, {\left(d x + c\right)} B a^{2} - 24 \, {\left(d x + c\right)} C a^{2} - 6 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{2} \sin\left(d x + c\right) - 24 \, B a^{2} \sin\left(d x + c\right) - 12 \, C a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 12*(d*x + c)*B*a^2 - 24*(d*x + c)*C*a^2 - 6*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*A*a^2*sin(d*x + c) - 24*B*a^2*sin(d*x + c) - 12*C*a^2*sin(d*x + c))/d","A",0
424,1,190,0,0.410839," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 96 \, {\left(d x + c\right)} C a^{2} - 96 \, B a^{2} \sin\left(d x + c\right) - 192 \, C a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(64*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 96*(d*x + c)*C*a^2 - 96*B*a^2*sin(d*x + c) - 192*C*a^2*sin(d*x + c))/d","A",0
425,1,236,0,0.371730," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 480 \, C a^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 480*C*a^2*sin(d*x + c))/d","A",0
426,1,296,0,0.377308," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{128 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{2} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} + 60 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2}}{960 \, d}"," ",0,"1/960*(128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^2 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 + 60*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2)/d","A",0
427,1,649,0,0.393785," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{224 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{3} + 3360 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 672 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{3} + 1120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 96 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} C a^{3} + 672 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{3} - 35 \, B a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 105 \, C a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 630 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 630 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{3360 \, d}"," ",0,"1/3360*(224*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^3 + 3360*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 672*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3 + 1120*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 96*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*C*a^3 + 672*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^3 - 35*B*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 105*C*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 630*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 630*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 210*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","B",0
428,1,559,0,0.423926," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{3} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 5 \, C a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(480*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^3 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 5*C*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 360*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^3*tan(d*x + c))/d","B",0
429,1,439,0,0.399010," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 15 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 45 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 720 \, A a^{3} \tan\left(d x + c\right) + 240 \, B a^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 15*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 45*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 720*A*a^3*tan(d*x + c) + 240*B*a^3*tan(d*x + c))/d","B",0
430,1,352,0,0.392985," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} A a^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 3 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, B a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 144 \, A a^{3} \tan\left(d x + c\right) + 144 \, B a^{3} \tan\left(d x + c\right) + 48 \, C a^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(d*x + c)*A*a^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 3*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 144*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 48*B*a^3*log(sec(d*x + c) + tan(d*x + c)) + 144*A*a^3*tan(d*x + c) + 144*B*a^3*tan(d*x + c) + 48*C*a^3*tan(d*x + c))/d","B",0
431,1,274,0,0.400250," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{36 \, {\left(d x + c\right)} A a^{3} + 12 \, {\left(d x + c\right)} B a^{3} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 3 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 9 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right) + 36 \, B a^{3} \tan\left(d x + c\right) + 36 \, C a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(36*(d*x + c)*A*a^3 + 12*(d*x + c)*B*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 3*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 9*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 18*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c) + 36*B*a^3*tan(d*x + c) + 36*C*a^3*tan(d*x + c))/d","A",0
432,1,237,0,0.466139," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 12 \, {\left(d x + c\right)} A a^{3} + 12 \, {\left(d x + c\right)} B a^{3} + 4 \, {\left(d x + c\right)} C a^{3} - C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 4 \, B a^{3} \sin\left(d x + c\right) + 4 \, B a^{3} \tan\left(d x + c\right) + 12 \, C a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 12*(d*x + c)*A*a^3 + 12*(d*x + c)*B*a^3 + 4*(d*x + c)*C*a^3 - C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 4*B*a^3*sin(d*x + c) + 4*B*a^3*tan(d*x + c) + 12*C*a^3*tan(d*x + c))/d","A",0
433,1,210,0,0.366797," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 12 \, {\left(d x + c\right)} A a^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 36 \, {\left(d x + c\right)} B a^{3} - 36 \, {\left(d x + c\right)} C a^{3} - 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 18 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, A a^{3} \sin\left(d x + c\right) - 36 \, B a^{3} \sin\left(d x + c\right) - 12 \, C a^{3} \sin\left(d x + c\right) - 12 \, C a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 12*(d*x + c)*A*a^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 36*(d*x + c)*B*a^3 - 36*(d*x + c)*C*a^3 - 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 18*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*A*a^3*sin(d*x + c) - 36*B*a^3*sin(d*x + c) - 12*C*a^3*sin(d*x + c) - 12*C*a^3*tan(d*x + c))/d","A",0
434,1,240,0,0.356654," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 96 \, {\left(d x + c\right)} B a^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 288 \, {\left(d x + c\right)} C a^{3} - 48 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 96 \, A a^{3} \sin\left(d x + c\right) - 288 \, B a^{3} \sin\left(d x + c\right) - 288 \, C a^{3} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(96*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 96*(d*x + c)*B*a^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 288*(d*x + c)*C*a^3 - 48*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 96*A*a^3*sin(d*x + c) - 288*B*a^3*sin(d*x + c) - 288*C*a^3*sin(d*x + c))/d","A",0
435,1,282,0,0.349558," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 480 \, {\left(d x + c\right)} C a^{3} + 480 \, B a^{3} \sin\left(d x + c\right) + 1440 \, C a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 480*(d*x + c)*C*a^3 + 480*B*a^3*sin(d*x + c) + 1440*C*a^3*sin(d*x + c))/d","A",0
436,1,354,0,0.353327," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 960 \, C a^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 960*C*a^3*sin(d*x + c))/d","A",0
437,1,425,0,0.357541," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} A a^{3} - 1344 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} + 105 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 1344 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 2240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 630 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{3} + 6720 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 630 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3}}{6720 \, d}"," ",0,"-1/6720*(192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*A*a^3 - 1344*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 + 105*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 1344*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^3 + 2240*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 630*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 + 6720*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 630*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3)/d","A",0
438,1,731,0,0.450356," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{224 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{4} + 6720 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 896 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{4} + 4480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 96 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} C a^{4} + 1344 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 1120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 35 \, B a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 140 \, C a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 1260 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3360 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3360 \, A a^{4} \tan\left(d x + c\right)}{3360 \, d}"," ",0,"1/3360*(224*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^4 + 6720*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 896*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^4 + 4480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 96*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*C*a^4 + 1344*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 1120*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 35*B*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 140*C*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 840*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 1260*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 3360*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 840*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 3360*A*a^4*tan(d*x + c))/d","B",0
439,1,638,0,0.449592," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{4} + 960 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 128 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 5 \, C a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 720 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 480 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 1920 \, A a^{4} \tan\left(d x + c\right) + 480 \, B a^{4} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^4 + 960*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 5*C*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 720*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 480*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 1920*A*a^4*tan(d*x + c) + 480*B*a^4*tan(d*x + c))/d","B",0
440,1,482,0,0.370586," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 240 \, {\left(d x + c\right)} A a^{4} + 320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 15 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 960 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 240 \, B a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 1440 \, A a^{4} \tan\left(d x + c\right) + 960 \, B a^{4} \tan\left(d x + c\right) + 240 \, C a^{4} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 240*(d*x + c)*A*a^4 + 320*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 15*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 240*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 360*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 240*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 960*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 240*B*a^4*log(sec(d*x + c) + tan(d*x + c)) + 1440*A*a^4*tan(d*x + c) + 960*B*a^4*tan(d*x + c) + 240*C*a^4*tan(d*x + c))/d","B",0
441,1,416,0,0.363662," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{192 \, {\left(d x + c\right)} A a^{4} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 48 \, {\left(d x + c\right)} B a^{4} + 64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 3 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 48 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{4} \sin\left(d x + c\right) + 192 \, A a^{4} \tan\left(d x + c\right) + 288 \, B a^{4} \tan\left(d x + c\right) + 192 \, C a^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(192*(d*x + c)*A*a^4 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 48*(d*x + c)*B*a^4 + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 3*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 48*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 72*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 144*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^4*sin(d*x + c) + 192*A*a^4*tan(d*x + c) + 288*B*a^4*tan(d*x + c) + 192*C*a^4*tan(d*x + c))/d","B",0
442,1,320,0,0.359544," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 72 \, {\left(d x + c\right)} A a^{4} + 48 \, {\left(d x + c\right)} B a^{4} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 12 \, {\left(d x + c\right)} C a^{4} - 3 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{4} \sin\left(d x + c\right) + 12 \, B a^{4} \sin\left(d x + c\right) + 12 \, A a^{4} \tan\left(d x + c\right) + 48 \, B a^{4} \tan\left(d x + c\right) + 72 \, C a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 72*(d*x + c)*A*a^4 + 48*(d*x + c)*B*a^4 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 12*(d*x + c)*C*a^4 - 3*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^4*sin(d*x + c) + 12*B*a^4*sin(d*x + c) + 12*A*a^4*tan(d*x + c) + 48*B*a^4*tan(d*x + c) + 72*C*a^4*tan(d*x + c))/d","A",0
443,1,296,0,0.365173," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 48 \, {\left(d x + c\right)} A a^{4} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 72 \, {\left(d x + c\right)} B a^{4} - 48 \, {\left(d x + c\right)} C a^{4} + 3 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, A a^{4} \sin\left(d x + c\right) - 48 \, B a^{4} \sin\left(d x + c\right) - 12 \, C a^{4} \sin\left(d x + c\right) - 12 \, B a^{4} \tan\left(d x + c\right) - 48 \, C a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 48*(d*x + c)*A*a^4 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 72*(d*x + c)*B*a^4 - 48*(d*x + c)*C*a^4 + 3*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 6*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 24*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 72*A*a^4*sin(d*x + c) - 48*B*a^4*sin(d*x + c) - 12*C*a^4*sin(d*x + c) - 12*B*a^4*tan(d*x + c) - 48*C*a^4*tan(d*x + c))/d","A",0
444,1,290,0,0.352186," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 96 \, {\left(d x + c\right)} A a^{4} + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} - 96 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 384 \, {\left(d x + c\right)} B a^{4} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 576 \, {\left(d x + c\right)} C a^{4} - 48 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 192 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 384 \, A a^{4} \sin\left(d x + c\right) - 576 \, B a^{4} \sin\left(d x + c\right) - 384 \, C a^{4} \sin\left(d x + c\right) - 96 \, C a^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(128*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 96*(d*x + c)*A*a^4 + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 - 96*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 384*(d*x + c)*B*a^4 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 576*(d*x + c)*C*a^4 - 48*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 192*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 384*A*a^4*sin(d*x + c) - 576*B*a^4*sin(d*x + c) - 384*C*a^4*sin(d*x + c) - 96*C*a^4*tan(d*x + c))/d","A",0
445,1,332,0,0.350446," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 60 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 480 \, {\left(d x + c\right)} B a^{4} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 1920 \, {\left(d x + c\right)} C a^{4} + 240 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{4} \sin\left(d x + c\right) + 1920 \, B a^{4} \sin\left(d x + c\right) + 2880 \, C a^{4} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 60*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 + 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 + 480*(d*x + c)*B*a^4 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 1920*(d*x + c)*C*a^4 + 240*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 480*A*a^4*sin(d*x + c) + 1920*B*a^4*sin(d*x + c) + 2880*C*a^4*sin(d*x + c))/d","A",0
446,1,400,0,0.362532," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{256 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 180 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} - 1920 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} + 120 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 960 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 960 \, {\left(d x + c\right)} C a^{4} + 960 \, B a^{4} \sin\left(d x + c\right) + 3840 \, C a^{4} \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 - 1920*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 120*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 + 960*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 + 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 960*(d*x + c)*C*a^4 + 960*B*a^4*sin(d*x + c) + 3840*C*a^4*sin(d*x + c))/d","B",0
447,1,483,0,0.370615," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} A a^{4} - 2688 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} + 140 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 2240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1792 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 8960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} - 1260 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} + 13440 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} - 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 6720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 6720 \, C a^{4} \sin\left(d x + c\right)}{6720 \, d}"," ",0,"-1/6720*(192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*A*a^4 - 2688*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 + 140*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 + 2240*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 1792*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^4 + 8960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 - 1260*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 13440*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 6720*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 6720*C*a^4*sin(d*x + c))/d","A",0
448,1,579,0,0.361883," ","integrate(cos(d*x+c)^8*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{12288 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} A a^{4} - 28672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} + 35 \, {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 3360 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 3360 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 3072 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} B a^{4} - 43008 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} + 2240 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 35840 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} - 13440 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 28672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} + 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 143360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} - 20160 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 26880 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4}}{107520 \, d}"," ",0,"-1/107520*(12288*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*A*a^4 - 28672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 + 35*(128*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c - 3*sin(8*d*x + 8*c) - 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*A*a^4 + 3360*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 3360*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 3072*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*B*a^4 - 43008*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 + 2240*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^4 + 35840*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 - 13440*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 28672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 560*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^4 + 143360*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 20160*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 26880*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4)/d","B",0
449,1,611,0,0.358676," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, {\left(\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a - \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{45 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{24 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 4 \, B {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 12 \, A {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{24 \, d}"," ",0,"-1/24*(C*(2*(21*sin(d*x + c)/(cos(d*x + c) + 1) - 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a - 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 45*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 24*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 4*B*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 12*A*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
450,1,485,0,0.357094," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, B {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 6 \, A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*B*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 6*A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
451,1,356,0,0.355220," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 2 \, B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 2 \, A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*(C*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 2*B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 2*A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
452,1,218,0,0.340507," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{A \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - A*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
453,1,146,0,0.490309," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{B \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
454,1,165,0,0.448679," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{C \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
455,1,273,0,0.441721," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(A*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
456,1,400,0,0.459606," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, B {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{3 \, d}"," ",0,"1/3*(A*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*B*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
457,1,525,0,0.477090," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 4 \, B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 12 \, C {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{12 \, d}"," ",0,"-1/12*(A*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 4*B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 12*C*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
458,1,567,0,0.370316," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 - 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 30*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 30*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + A*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
459,1,431,0,0.453132," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) + A*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2))/d","B",0
460,1,287,0,0.341504," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(C*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + A*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
461,1,190,0,0.461799," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - A*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
462,1,164,0,0.443847," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(A*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - C*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - B*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
463,1,235,0,0.486205," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(A*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - B*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + C*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
464,1,352,0,0.515045," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(A*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) + C*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
465,1,487,0,0.583974," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(A*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + C*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
466,1,493,0,0.489700," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - 3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(C*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - 3*B*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","B",0
467,1,350,0,0.422233," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*C*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + A*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","B",0
468,1,232,0,0.372526," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{3 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(C*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 3*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
469,1,179,0,0.392564," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, B {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(C*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + A*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + 3*B*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
470,1,205,0,0.479865," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - \frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{3 \, C {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(A*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 3*C*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
471,1,295,0,0.450918," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, A {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*A*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + C*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","B",0
472,1,411,0,0.459530," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - 3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(A*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - 3*B*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + C*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
473,1,547,0,0.466625," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{A {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{1380 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - B {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + 3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(A*(20*(33*sin(d*x + c)/(cos(d*x + c) + 1) + 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 51*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3 + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (735*sin(d*x + c)/(cos(d*x + c) + 1) - 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 1380*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 3*C*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
474,1,556,0,0.388979," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, C {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} - \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - B {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + 5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*C*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 - 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) + 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - B*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4))/d","B",0
475,1,411,0,0.381535," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - 5 \, B {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - 5*B*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","B",0
476,1,313,0,0.385115," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - \frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} - \frac{3 \, B {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - A*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3*B*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
477,1,259,0,0.369285," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{B {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(B*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + A*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
478,1,259,0,0.415926," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{B {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + B*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
479,1,286,0,0.473653," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - \frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} - \frac{3 \, B {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - C*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3*B*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","B",0
480,1,356,0,0.524987," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - 5 \, B {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - 5*B*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","B",0
481,1,474,0,0.489490," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, A {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} + \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{5880 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - B {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + 5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*A*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 + 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 5880*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - B*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4))/d","B",0
482,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,1,939,0,0.646927," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{4 \, B \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A}{4 \, d}"," ",0,"1/4*(4*B*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A)/d","B",0
488,1,1996,0,0.829376," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{16 \, C \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + 4 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B}{16 \, d}"," ",0,"1/16*(16*C*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + 4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B)/d","B",0
489,1,3770,0,1.210531," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} A + 6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B + 24 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*((4*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(3/4)*(cos(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(3*d*x + 3*c) - (cos(3*d*x + 3*c) - 1)*sin(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 6*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*((sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 15*sqrt(a)*(arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) + 1) - arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) - 1) - arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - 1)))*A + 6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B + 24*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
490,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,1,1801,0,0.751798," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A + \frac{2 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} B}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}}{4 \, d}"," ",0,"1/4*((2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A + 2*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/d","B",0
496,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,1,2780,0,0.825920," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(18 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(4 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + 5 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(4 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} \cos\left(d x + c\right) + 5 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left({\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \cos\left(d x + c\right) + {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 5 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{2 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(3*(18*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((4*a^2*sin(3*d*x + 3*c) + 5*a^2*sin(2*d*x + 2*c) + 4*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*cos(2*d*x + 2*c)^2*sin(d*x + c) + a^2*sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*a^2*cos(2*d*x + 2*c)*sin(d*x + c) + a^2*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (4*a^2*cos(3*d*x + 3*c) + 5*a^2*cos(2*d*x + 2*c) + 4*a^2*cos(d*x + c) + 5*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c)^2 + a^2*cos(d*x + c) + (a^2*cos(d*x + c) - a^2)*sin(2*d*x + 2*c)^2 - a^2 + 2*(a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 5*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 2*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
505,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
513,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
514,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
515,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
516,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
517,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
519,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
523,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
525,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
526,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
527,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
533,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
534,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
536,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
537,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
539,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
540,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
543,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
544,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
545,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
552,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
553,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
560,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
561,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
562,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
563,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
564,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
565,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
577,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,1,6492,0,1.342676," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{8 \, {\left(60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + 8*(60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + (420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(15/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(13/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(15/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(13/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
579,1,4002,0,1.026233," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{6 \, {\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 6*(12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + (60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
580,1,2167,0,0.884384," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{8 \, A \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} - \frac{4 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{16 \, d}"," ",0,"1/16*(8*A*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)) - 4*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
581,1,923,0,0.773281," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) + 2*B*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)) - (4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
582,1,373,0,0.742297," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 12 \, \sqrt{2} B \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, C \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)}}{6 \, d}"," ",0,"1/6*(sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) + 12*sqrt(2)*B*sqrt(a)*sin(1/2*d*x + 1/2*c) + 3*C*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)))/d","B",0
583,1,335,0,0.716640," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 10 \, \sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 120 \, \sqrt{2} C \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{60 \, d}"," ",0,"1/60*(sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 10*sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*B*sqrt(a) + 120*sqrt(2)*C*sqrt(a)*sin(1/2*d*x + 1/2*c))/d","B",0
584,1,609,0,0.754591," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(105 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 35 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 105 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 35 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 7 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 10 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 14 \, \sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 140 \, \sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(3*sqrt(2)*(105*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 35*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 7*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 105*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 35*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 7*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 10*sin(7/2*d*x + 7/2*c) + 7*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 14*sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*B*sqrt(a) + 140*sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a))/d","B",0
585,1,878,0,0.787934," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(1890 \, \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 420 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 252 \, \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 1890 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 420 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 252 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 45 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 252 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 420 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1890 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 18 \, \sqrt{2} {\left(105 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 35 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 105 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 35 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 7 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 10 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 84 \, \sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(1890*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 420*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 252*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 45*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 1890*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 420*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 252*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 45*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*sin(9/2*d*x + 9/2*c) + 45*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 252*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 420*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1890*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) + 18*sqrt(2)*(105*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 35*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 7*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 105*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 35*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 7*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 10*sin(7/2*d*x + 7/2*c) + 7*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*B*sqrt(a) + 84*sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*C*sqrt(a))/d","B",0
586,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,1,8121,0,1.506613," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1} + \frac{8 \, {\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{3 \, {\left(300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 8*(132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + 3*(300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
588,1,5748,0,1.136284," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{6 \, {\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1} - \frac{{\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"1/96*(24*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - 6*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*B*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
589,1,3661,0,0.974023," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + \frac{4 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} B \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1}}{16 \, d}"," ",0,"1/16*(4*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 4*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*B*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1))/d","B",0
590,1,1455,0,0.813756," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 4 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + \frac{3 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(3*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 4*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 3*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
591,1,522,0,0.797954," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 15 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a} + 20 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a}}{60 \, d}"," ",0,"1/60*(3*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 15*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a) + 20*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a))/d","B",0
592,1,550,0,0.786282," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 42 \, \sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 280 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 42*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*B*sqrt(a) + 280*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","B",0
593,1,908,0,0.837585," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3780 \, a \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1050 \, a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 378 \, a \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 3780 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 1050 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 378 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 135 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 378 \, a \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1050 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 3780 \, a \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 6 \, \sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 252 \, \sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(3780*a*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 1050*a*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 378*a*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 135*a*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 3780*a*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 1050*a*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 378*a*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 135*a*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a*sin(9/2*d*x + 9/2*c) + 135*a*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 378*a*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1050*a*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 3780*a*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) + 6*sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*B*sqrt(a) + 252*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*C*sqrt(a))/d","B",0
594,1,1188,0,0.862789," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{21 \, \sqrt{2} {\left(3630 \, a \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 990 \, a \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 429 \, a \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 165 \, a \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 3630 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 990 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 429 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 165 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 55 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 165 \, a \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 429 \, a \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 990 \, a \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3630 \, a \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 22 \, \sqrt{2} {\left(3780 \, a \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1050 \, a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 378 \, a \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 3780 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 1050 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 378 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 135 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 378 \, a \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1050 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 3780 \, a \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 132 \, \sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{110880 \, d}"," ",0,"1/110880*(21*sqrt(2)*(3630*a*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 990*a*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 429*a*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 165*a*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 55*a*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 3630*a*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 990*a*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 429*a*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 165*a*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 55*a*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 30*a*sin(11/2*d*x + 11/2*c) + 55*a*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 165*a*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 429*a*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 990*a*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3630*a*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) + 22*sqrt(2)*(3780*a*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 1050*a*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 378*a*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 135*a*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 3780*a*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 1050*a*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 378*a*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 135*a*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a*sin(9/2*d*x + 9/2*c) + 135*a*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 378*a*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1050*a*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 3780*a*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*B*sqrt(a) + 132*sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*C*sqrt(a))/d","B",0
595,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,1,976,0,0.838795," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{5 \, \sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 70 \, \sqrt{2} {\left(30 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 30 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a} + 28 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a}}{840 \, d}"," ",0,"1/840*(5*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 70*sqrt(2)*(30*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 30*a^2*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*a^2*sin(3/2*d*x + 3/2*c) + 30*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a) + 28*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*B*sqrt(a))/d","B",0
602,1,804,0,0.801430," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 30 \, \sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 168 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) + 30*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*B*sqrt(a) + 168*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","B",0
603,1,1266,0,0.857207," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{5 \, \sqrt{2} {\left(31878 \, a^{2} \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 8778 \, a^{2} \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 3465 \, a^{2} \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1287 \, a^{2} \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 31878 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 8778 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 3465 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1287 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 385 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 126 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1287 \, a^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3465 \, a^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 8778 \, a^{2} \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 31878 \, a^{2} \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 22 \, \sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 660 \, \sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{110880 \, d}"," ",0,"1/110880*(5*sqrt(2)*(31878*a^2*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 8778*a^2*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 3465*a^2*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 1287*a^2*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 385*a^2*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 31878*a^2*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 8778*a^2*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 3465*a^2*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1287*a^2*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 385*a^2*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 126*a^2*sin(11/2*d*x + 11/2*c) + 385*a^2*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1287*a^2*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3465*a^2*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 8778*a^2*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 31878*a^2*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) + 22*sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*B*sqrt(a) + 660*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*C*sqrt(a))/d","B",0
604,1,1562,0,0.881910," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3783780 \, a^{2} \cos\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 1066065 \, a^{2} \cos\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 459459 \, a^{2} \cos\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 193050 \, a^{2} \cos\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 70070 \, a^{2} \cos\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \cos\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 3783780 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 1066065 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 459459 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 193050 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 70070 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 20475 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 6930 \, a^{2} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \sin\left(\frac{11}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 70070 \, a^{2} \sin\left(\frac{9}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 193050 \, a^{2} \sin\left(\frac{7}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 459459 \, a^{2} \sin\left(\frac{5}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 1066065 \, a^{2} \sin\left(\frac{3}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 3783780 \, a^{2} \sin\left(\frac{1}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 130 \, \sqrt{2} {\left(31878 \, a^{2} \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 8778 \, a^{2} \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 3465 \, a^{2} \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1287 \, a^{2} \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 31878 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 8778 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 3465 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1287 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 385 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 126 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1287 \, a^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3465 \, a^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 8778 \, a^{2} \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 31878 \, a^{2} \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} B \sqrt{a} + 572 \, \sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{2882880 \, d}"," ",0,"1/2882880*(sqrt(2)*(3783780*a^2*cos(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 1066065*a^2*cos(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 459459*a^2*cos(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 193050*a^2*cos(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 70070*a^2*cos(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 20475*a^2*cos(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) - 3783780*a^2*cos(13/2*d*x + 13/2*c)*sin(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 1066065*a^2*cos(13/2*d*x + 13/2*c)*sin(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 459459*a^2*cos(13/2*d*x + 13/2*c)*sin(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 193050*a^2*cos(13/2*d*x + 13/2*c)*sin(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 70070*a^2*cos(13/2*d*x + 13/2*c)*sin(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 20475*a^2*cos(13/2*d*x + 13/2*c)*sin(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 6930*a^2*sin(13/2*d*x + 13/2*c) + 20475*a^2*sin(11/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 70070*a^2*sin(9/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 193050*a^2*sin(7/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 459459*a^2*sin(5/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 1066065*a^2*sin(3/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 3783780*a^2*sin(1/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))))*A*sqrt(a) + 130*sqrt(2)*(31878*a^2*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 8778*a^2*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 3465*a^2*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 1287*a^2*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 385*a^2*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 31878*a^2*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 8778*a^2*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 3465*a^2*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1287*a^2*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 385*a^2*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 126*a^2*sin(11/2*d*x + 11/2*c) + 385*a^2*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1287*a^2*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3465*a^2*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 8778*a^2*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 31878*a^2*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*B*sqrt(a) + 572*sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*C*sqrt(a))/d","B",0
605,1,5206,0,1.147674," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} - \frac{6 \, {\left(4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} + \frac{{\left(84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C}{{\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)) - 6*(4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(a)) + (84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
606,1,2998,0,0.996722," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} A}{\sqrt{a}} + \frac{4 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} - \frac{{\left(4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{16 \, d}"," ",0,"-1/16*(8*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*A/sqrt(a) + 4*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)) - (4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
607,1,1442,0,0.886007," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} A}{\sqrt{a}} - \frac{2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} B}{\sqrt{a}} - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*(2*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*A/sqrt(a) - 2*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*B/sqrt(a) - (4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
608,1,668,0,0.789869," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{\sqrt{a}} - \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} B}{\sqrt{a}} + \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} C}{\sqrt{a}}}{2 \, d}"," ",0,"-1/2*((sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*A/sqrt(a) - (sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*B/sqrt(a) + (sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*C/sqrt(a))/d","B",0
609,1,475,0,0.758737," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} + \frac{3 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B}{\sqrt{a}} - \frac{3 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} C}{\sqrt{a}}}{6 \, d}"," ",0,"-1/6*((3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A/sqrt(a) + 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*B/sqrt(a) - 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*C/sqrt(a))/d","B",0
610,1,742,0,0.798811," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{2} {\left(60 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 60 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 60 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{10 \, {\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} B}{\sqrt{a}} - \frac{30 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C}{\sqrt{a}}}{60 \, d}"," ",0,"1/60*(sqrt(2)*(60*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 60*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 6*sin(5/2*d*x + 5/2*c) - 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 60*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A/sqrt(a) - 10*(3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*B/sqrt(a) - 30*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*C/sqrt(a))/d","B",0
611,1,1085,0,0.860976," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{2} {\left(525 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 175 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 525 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) + 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) - 30 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 525 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{14 \, \sqrt{2} {\left(60 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 60 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 60 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} B}{\sqrt{a}} + \frac{140 \, {\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C}{\sqrt{a}}}{840 \, d}"," ",0,"-1/840*(sqrt(2)*(525*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 175*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 525*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) + 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 - 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) - 30*sin(7/2*d*x + 7/2*c) + 21*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 525*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A/sqrt(a) - 14*sqrt(2)*(60*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 60*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 6*sin(5/2*d*x + 5/2*c) - 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 60*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*B/sqrt(a) + 140*(3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C/sqrt(a))/d","B",0
612,1,1918,0,1.032398," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} A \sqrt{a} - 2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} B \sqrt{a} - \frac{2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} A b}{\sqrt{a}} - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B b}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*(2*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*A*sqrt(a) - 2*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*B*sqrt(a) - 2*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*A*b/sqrt(a) - (4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*b/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
613,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
619,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
626,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
627,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(4/3), x)","F",0
628,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(7/3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(1/3), x)","F",0
631,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(2/3), x)","F",0
632,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^m, x)","F",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{-n - 1}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
635,1,310,0,6.693541," ","integrate((a+a*sec(d*x+c))^n*(-a*(A*n+B*n+B)-a*C*(1+n)*sec(d*x+c))/a/(1+n)/(sec(d*x+c)^n)+sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(-{\left(d n + d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - c\right) \sin\left(c n\right) - {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(-{\left(d n - d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + c\right) \sin\left(c n\right) - {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(c n\right) \sin\left(-{\left(d n + d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - c\right) + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} A a^{n} \cos\left(c n\right) \sin\left(-{\left(d n - d\right)} x + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + c\right)}{2 \, {\left({\left(d n + d\right)} 2^{n} \cos\left(c n\right)^{2} + {\left(d n + d\right)} 2^{n} \sin\left(c n\right)^{2}\right)}}"," ",0,"1/2*((cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(-(d*n + d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) - c)*sin(c*n) - (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(-(d*n - d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) + c)*sin(c*n) - (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(c*n)*sin(-(d*n + d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) - c) + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*A*a^n*cos(c*n)*sin(-(d*n - d)*x + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1) + c))/((d*n + d)*2^n*cos(c*n)^2 + (d*n + d)*2^n*sin(c*n)^2)","B",0
636,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^m*(B-C+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + B - C\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + B - C)*(a*sec(d*x + c) + a)^m, x)","F",0
637,1,175,0,0.361117," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b - 15 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b - 15*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
638,1,152,0,0.360075," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, C b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*C*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a*tan(d*x + c))/d","A",0
639,1,100,0,0.346715," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, A b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*A*a*log(sec(d*x + c) + tan(d*x + c)) + 12*A*b*tan(d*x + c))/d","A",0
640,1,88,0,0.335387," ","integrate((a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a - C b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, C a \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a - C*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*A*b*log(sec(d*x + c) + tan(d*x + c)) + 4*C*a*tan(d*x + c))/d","A",0
641,1,59,0,0.347143," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} A b + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a \sin\left(d x + c\right) + 2 \, C b \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*A*b + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a*sin(d*x + c) + 2*C*b*tan(d*x + c))/d","A",0
642,1,70,0,0.348293," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 4 \, {\left(d x + c\right)} C a + 2 \, C b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a + 4*(d*x + c)*C*a + 2*C*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*b*sin(d*x + c))/d","A",0
643,1,67,0,0.355943," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b - 12 \, {\left(d x + c\right)} C b - 12 \, C a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b - 12*(d*x + c)*C*b - 12*C*a*sin(d*x + c))/d","A",0
644,1,90,0,0.353556," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b + 96 \, C b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b + 96*C*b*sin(d*x + c))/d","A",0
645,1,113,0,0.354671," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*b)/d","A",0
646,1,216,0,0.360749," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{2} + 8 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{2} - 15 \, C a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, A a^{2} \tan\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(40*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^2 + 8*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^2 - 15*C*a*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*A*a^2*tan(d*x + c))/d","A",0
647,1,225,0,0.362000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b - 3 \, C b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 96 \, A a b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b - 3*C*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 96*A*a*b*tan(d*x + c))/d","A",0
648,1,129,0,0.359814," ","integrate((a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} A a^{2} + 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{2} - 3 \, C a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 6 \, C a^{2} \tan\left(d x + c\right) + 6 \, A b^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*A*a^2 + 2*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^2 - 3*C*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*A*a*b*log(sec(d*x + c) + tan(d*x + c)) + 6*C*a^2*tan(d*x + c) + 6*A*b^2*tan(d*x + c))/d","A",0
649,1,140,0,0.368062," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} A a b - C b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a^{2} \sin\left(d x + c\right) + 8 \, C a b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*A*a*b - C*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a^2*sin(d*x + c) + 8*C*a*b*tan(d*x + c))/d","A",0
650,1,99,0,0.359593," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 4 \, {\left(d x + c\right)} A b^{2} + 4 \, C a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, A a b \sin\left(d x + c\right) + 4 \, C b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 4*(d*x + c)*C*a^2 + 4*(d*x + c)*A*b^2 + 4*C*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*A*a*b*sin(d*x + c) + 4*C*b^2*tan(d*x + c))/d","A",0
651,1,112,0,0.350173," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b - 12 \, {\left(d x + c\right)} C a b - 3 \, C b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, C a^{2} \sin\left(d x + c\right) - 6 \, A b^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b - 12*(d*x + c)*C*a*b - 3*C*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*C*a^2*sin(d*x + c) - 6*A*b^2*sin(d*x + c))/d","A",0
652,1,130,0,0.355770," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{2} + 96 \, {\left(d x + c\right)} C b^{2} + 192 \, C a b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^2 + 96*(d*x + c)*C*b^2 + 192*C*a*b*sin(d*x + c))/d","A",0
653,1,154,0,0.362471," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{2} + 240 \, C b^{2} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2 - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^2 + 240*C*b^2*sin(d*x + c))/d","A",0
654,1,386,0,0.373916," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{2} + 96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a b^{2} - 5 \, C b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, C a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, A a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(160*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^2 + 96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a*b^2 - 5*C*b^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 90*C*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*A*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 360*A*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^3*tan(d*x + c))/d","A",0
655,1,289,0,0.364376," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{3} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{3} - 45 \, C a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, A a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 720 \, A a^{2} b \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^3 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^3 - 45*C*a*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*A*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 720*A*a^2*b*tan(d*x + c))/d","A",0
656,1,254,0,0.353588," ","integrate((a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} A a^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b^{2} - C b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, A b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{2} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 16 \, C a^{3} \tan\left(d x + c\right) + 48 \, A a b^{2} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(d*x + c)*A*a^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b^2 - C*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*A*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a^2*b*log(sec(d*x + c) + tan(d*x + c)) + 16*C*a^3*tan(d*x + c) + 48*A*a*b^2*tan(d*x + c))/d","A",0
657,1,181,0,0.368800," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{36 \, {\left(d x + c\right)} A a^{2} b + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{3} - 9 \, C a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, A a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 36 \, C a^{2} b \tan\left(d x + c\right) + 12 \, A b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(36*(d*x + c)*A*a^2*b + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^3 - 9*C*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*A*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 36*C*a^2*b*tan(d*x + c) + 12*A*b^3*tan(d*x + c))/d","A",0
658,1,179,0,0.367869," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 4 \, {\left(d x + c\right)} C a^{3} + 12 \, {\left(d x + c\right)} A a b^{2} - C b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{2} b \sin\left(d x + c\right) + 12 \, C a b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 4*(d*x + c)*C*a^3 + 12*(d*x + c)*A*a*b^2 - C*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^2*b*sin(d*x + c) + 12*C*a*b^2*tan(d*x + c))/d","A",0
659,1,141,0,0.365045," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b - 36 \, {\left(d x + c\right)} C a^{2} b - 12 \, {\left(d x + c\right)} A b^{3} - 18 \, C a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{3} \sin\left(d x + c\right) - 36 \, A a b^{2} \sin\left(d x + c\right) - 12 \, C b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b - 36*(d*x + c)*C*a^2*b - 12*(d*x + c)*A*b^3 - 18*C*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*C*a^3*sin(d*x + c) - 36*A*a*b^2*sin(d*x + c) - 12*C*b^3*tan(d*x + c))/d","A",0
660,1,174,0,0.353205," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 8 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{2} + 96 \, {\left(d x + c\right)} C a b^{2} + 16 \, C b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, C a^{2} b \sin\left(d x + c\right) + 32 \, A b^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"1/32*((12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 + 8*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^2 + 96*(d*x + c)*C*a*b^2 + 16*C*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*C*a^2*b*sin(d*x + c) + 32*A*b^3*sin(d*x + c))/d","A",0
661,1,194,0,0.361109," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{3} + 480 \, {\left(d x + c\right)} C b^{3} + 1440 \, C a b^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2*b + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^3 + 480*(d*x + c)*C*b^3 + 1440*C*a*b^2*sin(d*x + c))/d","A",0
662,1,243,0,0.363137," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} b + 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{2} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{3} - 960 \, C b^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2*b + 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b^2 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^3 - 960*C*b^3*sin(d*x + c))/d","A",0
663,1,472,0,0.359251," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{280 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 1680 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 336 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{2} b^{2} + 56 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A b^{4} + 24 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} C b^{4} - 35 \, C a b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, C a^{3} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, A a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 840 \, A a^{4} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(280*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 1680*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b^2 + 336*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^2*b^2 + 56*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*b^4 + 24*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*C*b^4 - 35*C*a*b^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 210*C*a^3*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 210*A*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*A*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 840*A*a^4*tan(d*x + c))/d","A",0
664,1,459,0,0.363207," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} b + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{3} + 128 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a b^{3} - 5 \, C b^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 720 \, A a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 1920 \, A a^{3} b \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3*b + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^3 + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a*b^3 - 5*C*b^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 180*C*a^2*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*A*b^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 720*A*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 1920*A*a^3*b*tan(d*x + c))/d","A",0
665,1,318,0,0.364448," ","integrate((a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{60 \, {\left(d x + c\right)} A a^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b^{2} + 20 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{4} + 4 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{4} - 15 \, C a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{3} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 60 \, C a^{4} \tan\left(d x + c\right) + 360 \, A a^{2} b^{2} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*A*a^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b^2 + 20*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^4 + 4*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^4 - 15*C*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*A*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^3*b*log(sec(d*x + c) + tan(d*x + c)) + 60*C*a^4*tan(d*x + c) + 360*A*a^2*b^2*tan(d*x + c))/d","A",0
666,1,306,0,0.344018," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{192 \, {\left(d x + c\right)} A a^{3} b + 64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b^{3} - 3 \, C b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, C a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, A a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{4} \sin\left(d x + c\right) + 192 \, C a^{3} b \tan\left(d x + c\right) + 192 \, A a b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(192*(d*x + c)*A*a^3*b + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b^3 - 3*C*b^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 72*C*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 144*A*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^4*sin(d*x + c) + 192*C*a^3*b*tan(d*x + c) + 192*A*a*b^3*tan(d*x + c))/d","A",0
667,1,221,0,0.343142," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 12 \, {\left(d x + c\right)} C a^{4} + 72 \, {\left(d x + c\right)} A a^{2} b^{2} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{4} - 12 \, C a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{3} b \sin\left(d x + c\right) + 72 \, C a^{2} b^{2} \tan\left(d x + c\right) + 12 \, A b^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 12*(d*x + c)*C*a^4 + 72*(d*x + c)*A*a^2*b^2 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^4 - 12*C*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*A*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^3*b*sin(d*x + c) + 72*C*a^2*b^2*tan(d*x + c) + 12*A*b^4*tan(d*x + c))/d","A",0
668,1,221,0,0.351534," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 48 \, {\left(d x + c\right)} C a^{3} b - 48 \, {\left(d x + c\right)} A a b^{3} + 3 \, C b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, A b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} \sin\left(d x + c\right) - 72 \, A a^{2} b^{2} \sin\left(d x + c\right) - 48 \, C a b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3*b - 48*(d*x + c)*C*a^3*b - 48*(d*x + c)*A*a*b^3 + 3*C*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*C*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*A*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*C*a^4*sin(d*x + c) - 72*A*a^2*b^2*sin(d*x + c) - 48*C*a*b^3*tan(d*x + c))/d","A",0
669,1,204,0,0.363636," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} b + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b^{2} + 576 \, {\left(d x + c\right)} C a^{2} b^{2} + 96 \, {\left(d x + c\right)} A b^{4} + 192 \, C a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 384 \, C a^{3} b \sin\left(d x + c\right) + 384 \, A a b^{3} \sin\left(d x + c\right) + 96 \, C b^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3*b + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b^2 + 576*(d*x + c)*C*a^2*b^2 + 96*(d*x + c)*A*b^4 + 192*C*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 384*C*a^3*b*sin(d*x + c) + 384*A*a*b^3*sin(d*x + c) + 96*C*b^4*tan(d*x + c))/d","A",0
670,1,239,0,0.352762," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 40 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} + 480 \, {\left(d x + c\right)} C a b^{3} + 60 \, C b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 720 \, C a^{2} b^{2} \sin\left(d x + c\right) + 120 \, A b^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 40*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3*b + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3*b - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^3 + 480*(d*x + c)*C*a*b^3 + 60*C*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 720*C*a^2*b^2*sin(d*x + c) + 120*A*b^4*sin(d*x + c))/d","A",0
671,1,283,0,0.359678," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 256 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} b + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} b - 180 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b^{2} - 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b^{2} + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{3} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{4} - 960 \, {\left(d x + c\right)} C b^{4} - 3840 \, C a b^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3*b + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3*b - 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2*b^2 - 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b^2 + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^3 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^4 - 960*(d*x + c)*C*b^4 - 3840*C*a*b^3*sin(d*x + c))/d","A",0
672,1,329,0,0.362852," ","integrate(cos(d*x+c)^7*(a+b*sec(d*x+c))^4*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{48 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} A a^{4} - 112 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b - 672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} b^{2} + 3360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b^{2} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} - 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} + 560 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{4} - 1680 \, C b^{4} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"-1/1680*(48*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*A*a^4 - 112*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3*b - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3*b - 672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2*b^2 + 3360*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b^2 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b^3 - 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^3 + 560*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^4 - 1680*C*b^4*sin(d*x + c))/d","A",0
673,1,192,0,0.342530," ","integrate((a+b*sec(d*x+c))^3*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} a^{5} - 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{4} + b^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, a^{2} b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, a^{4} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 32 \, a^{3} b^{2} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(d*x + c)*a^5 - 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^4 + b^5*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 8*a^2*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*a^4*b*log(sec(d*x + c) + tan(d*x + c)) + 32*a^3*b^2*tan(d*x + c))/d","A",0
674,1,105,0,0.354835," ","integrate((a+b*sec(d*x+c))^2*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a^{4} - 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} b^{4} + 3 \, a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*a^4 - 2*(tan(d*x + c)^3 + 3*tan(d*x + c))*b^4 + 3*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*a^3*b*log(sec(d*x + c) + tan(d*x + c)))/d","A",0
675,1,93,0,0.359004," ","integrate((a+b*sec(d*x+c))*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} a^{3} + b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, a^{2} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 4 \, a b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*a^3 + b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*a^2*b*log(sec(d*x + c) + tan(d*x + c)) - 4*a*b^2*tan(d*x + c))/d","A",0
676,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
677,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
678,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
679,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
680,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
681,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
682,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
683,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
684,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
685,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
686,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
687,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
688,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
689,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
690,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
691,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
692,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
693,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
694,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
695,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
696,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
697,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
698,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
699,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
700,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
701,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
702,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
703,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
704,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
705,-2,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
706,-2,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
707,-2,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
708,-2,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
709,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
710,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
711,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
712,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
713,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
714,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
715,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
716,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
717,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
720,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
721,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
722,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
723,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
724,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
725,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
731,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
732,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(a^2-b^2*sec(d*x+c)^2),x, algorithm=""maxima"")","-\int {\left(b^{2} \sec\left(d x + c\right)^{2} - a^{2}\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"-integrate((b^2*sec(d*x + c)^2 - a^2)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
734,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\int {\left(b^{2} \sec\left(d x + c\right)^{2} - a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"-integrate((b^2*sec(d*x + c)^2 - a^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
735,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
737,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
738,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
739,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
740,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
741,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
742,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
748,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
754,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,0,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\int \frac{b^{2} \sec\left(d x + c\right)^{2} - a^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"-integrate((b^2*sec(d*x + c)^2 - a^2)/sqrt(b*sec(d*x + c) + a), x)","F",0
756,-1,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate((a^2-b^2*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
760,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
761,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
762,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(b*sec(d*x + c) + a)^(1/3), x)","F",0
763,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
764,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
765,1,200,0,0.348821," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b - 15 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b - 15*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
766,1,163,0,0.350781," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b - 3 \, C b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b - 3*C*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
767,1,127,0,0.359577," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*B*a*tan(d*x + c))/d","A",0
768,1,88,0,0.337887," ","integrate((a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{C b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, B a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 4 \, C a \tan\left(d x + c\right) - 4 \, B b \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(C*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*B*a*log(sec(d*x + c) + tan(d*x + c)) - 4*C*a*tan(d*x + c) - 4*B*b*tan(d*x + c))/d","A",0
769,1,73,0,0.350962," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + B b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C b \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + B*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*b*tan(d*x + c))/d","B",0
770,1,58,0,0.349808," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a + 2 \, {\left(d x + c\right)} B b + C b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + 2*(d*x + c)*B*b + C*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a*sin(d*x + c))/d","A",0
771,1,55,0,0.338615," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a + 4 \, {\left(d x + c\right)} C b + 4 \, C a \sin\left(d x + c\right) + 4 \, B b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a + 4*(d*x + c)*C*b + 4*C*a*sin(d*x + c) + 4*B*b*sin(d*x + c))/d","A",0
772,1,79,0,0.344129," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b - 12 \, C b \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b - 12*C*b*sin(d*x + c))/d","A",0
773,1,101,0,0.339211," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*b)/d","A",0
774,1,124,0,0.331876," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b)/d","A",0
775,1,276,0,0.364660," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{2} - 30 \, C a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^2 - 30*C*a*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
776,1,228,0,0.339377," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{2} - 3 \, C b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^2 - 3*C*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 24*B*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*B*a^2*tan(d*x + c))/d","A",0
777,1,165,0,0.329688," ","integrate((a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{2} - 6 \, C a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, C a^{2} \tan\left(d x + c\right) + 24 \, B a b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^2 - 6*C*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*B*a^2*log(sec(d*x + c) + tan(d*x + c)) + 12*C*a^2*tan(d*x + c) + 24*B*a*b*tan(d*x + c))/d","A",0
778,1,140,0,0.338192," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{2} - C b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, C a b \tan\left(d x + c\right) + 4 \, B b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a^2 - C*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*C*a*b*tan(d*x + c) + 4*B*b^2*tan(d*x + c))/d","A",0
779,1,103,0,0.336009," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a^{2} + 4 \, {\left(d x + c\right)} B a b + 2 \, C a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + B b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a^{2} \sin\left(d x + c\right) + 2 \, C b^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a^2 + 4*(d*x + c)*B*a*b + 2*C*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + B*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a^2*sin(d*x + c) + 2*C*b^2*tan(d*x + c))/d","A",0
780,1,99,0,0.333508," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 8 \, {\left(d x + c\right)} C a b + 4 \, {\left(d x + c\right)} B b^{2} + 2 \, C b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} \sin\left(d x + c\right) + 8 \, B a b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 + 8*(d*x + c)*C*a*b + 4*(d*x + c)*B*b^2 + 2*C*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^2*sin(d*x + c) + 8*B*a*b*sin(d*x + c))/d","A",0
781,1,108,0,0.338870," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b - 12 \, {\left(d x + c\right)} C b^{2} - 24 \, C a b \sin\left(d x + c\right) - 12 \, B b^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b - 12*(d*x + c)*C*b^2 - 24*C*a*b*sin(d*x + c) - 12*B*b^2*sin(d*x + c))/d","A",0
782,1,142,0,0.332736," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b + 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{2} + 96 \, C b^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b + 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^2 + 96*C*b^2*sin(d*x + c))/d","A",0
783,1,176,0,0.331546," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a b - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{2}}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a*b - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^2)/d","A",0
784,1,409,0,0.341881," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b + 96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a b^{2} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B b^{3} - 5 \, C b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, C a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, B a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"1/480*(160*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b + 96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a*b^2 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*b^3 - 5*C*b^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 90*C*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*B*a*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
785,1,341,0,0.333830," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{2} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{3} - 45 \, C a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, B a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, B a^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^2 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^3 - 45*C*a*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*B*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*B*a^3*tan(d*x + c))/d","A",0
786,1,266,0,0.338537," ","integrate((a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b^{2} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{3} - 3 \, C b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, C a^{3} \tan\left(d x + c\right) + 144 \, B a^{2} b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b^2 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^3 - 3*C*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 36*C*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*B*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*B*a^3*log(sec(d*x + c) + tan(d*x + c)) + 48*C*a^3*tan(d*x + c) + 144*B*a^2*b*tan(d*x + c))/d","A",0
787,1,216,0,0.336629," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{3} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{3} - 9 \, C a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, B a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, C a^{2} b \tan\left(d x + c\right) + 36 \, B a b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*B*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^3 - 9*C*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*B*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*C*a^2*b*tan(d*x + c) + 36*B*a*b^2*tan(d*x + c))/d","A",0
788,1,169,0,0.341743," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a^{3} + 12 \, {\left(d x + c\right)} B a^{2} b - C b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{3} \sin\left(d x + c\right) + 12 \, C a b^{2} \tan\left(d x + c\right) + 4 \, B b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a^3 + 12*(d*x + c)*B*a^2*b - C*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^3*sin(d*x + c) + 12*C*a*b^2*tan(d*x + c) + 4*B*b^3*tan(d*x + c))/d","A",0
789,1,144,0,0.342828," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 12 \, {\left(d x + c\right)} C a^{2} b + 12 \, {\left(d x + c\right)} B a b^{2} + 6 \, C a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{3} \sin\left(d x + c\right) + 12 \, B a^{2} b \sin\left(d x + c\right) + 4 \, C b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 12*(d*x + c)*C*a^2*b + 12*(d*x + c)*B*a*b^2 + 6*C*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^3*sin(d*x + c) + 12*B*a^2*b*sin(d*x + c) + 4*C*b^3*tan(d*x + c))/d","A",0
790,1,152,0,0.342645," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b - 36 \, {\left(d x + c\right)} C a b^{2} - 12 \, {\left(d x + c\right)} B b^{3} - 6 \, C b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{2} b \sin\left(d x + c\right) - 36 \, B a b^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b - 36*(d*x + c)*C*a*b^2 - 12*(d*x + c)*B*b^3 - 6*C*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*C*a^2*b*sin(d*x + c) - 36*B*a*b^2*sin(d*x + c))/d","A",0
791,1,171,0,0.340481," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{2} + 96 \, {\left(d x + c\right)} C b^{3} + 288 \, C a b^{2} \sin\left(d x + c\right) + 96 \, B b^{3} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 96*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^2 + 96*(d*x + c)*C*b^3 + 288*C*a*b^2*sin(d*x + c) + 96*B*b^3*sin(d*x + c))/d","A",0
792,1,217,0,0.350018," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{2} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} + 480 \, C b^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^2 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^3 + 480*C*b^3*sin(d*x + c))/d","A",0
793,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
794,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
795,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
796,-2,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
797,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
798,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
799,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
800,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
801,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
802,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
803,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
804,-2,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
805,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
806,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
807,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
808,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
809,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
810,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
811,-2,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
812,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
813,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
814,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
815,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
816,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
817,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
818,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
819,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
820,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
821,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
824,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2), x)","F",0
825,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
826,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
827,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
828,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
829,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
833,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
834,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
835,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
836,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^5, x)","F",0
837,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
839,0,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
840,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
841,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
842,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
843,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
845,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
846,-1,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
849,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
854,-1,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
856,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
857,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(2/3), x)","F",0
858,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*(b*sec(d*x + c) + a)^(1/3), x)","F",0
859,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(1/3), x)","F",0
860,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/(b*sec(d*x + c) + a)^(2/3), x)","F",0
861,1,266,0,0.356690," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b - 15 \, C a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b - 15*C*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
862,1,218,0,0.373541," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b - 3 \, C b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b - 3*C*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a*tan(d*x + c))/d","A",0
863,1,155,0,0.356012," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, B a \tan\left(d x + c\right) + 12 \, A b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*A*a*log(sec(d*x + c) + tan(d*x + c)) + 12*B*a*tan(d*x + c) + 12*A*b*tan(d*x + c))/d","A",0
864,1,116,0,0.337726," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a - C b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, A b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, C a \tan\left(d x + c\right) + 4 \, B b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a - C*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*B*a*log(sec(d*x + c) + tan(d*x + c)) + 4*A*b*log(sec(d*x + c) + tan(d*x + c)) + 4*C*a*tan(d*x + c) + 4*B*b*tan(d*x + c))/d","A",0
865,1,92,0,0.337771," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + 2 \, {\left(d x + c\right)} A b + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + B b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a \sin\left(d x + c\right) + 2 \, C b \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + 2*(d*x + c)*A*b + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + B*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a*sin(d*x + c) + 2*C*b*tan(d*x + c))/d","A",0
866,1,89,0,0.352937," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 4 \, {\left(d x + c\right)} C a + 4 \, {\left(d x + c\right)} B b + 2 \, C b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a \sin\left(d x + c\right) + 4 \, A b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a + 4*(d*x + c)*C*a + 4*(d*x + c)*B*b + 2*C*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a*sin(d*x + c) + 4*A*b*sin(d*x + c))/d","A",0
867,1,98,0,0.337888," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b - 12 \, {\left(d x + c\right)} C b - 12 \, C a \sin\left(d x + c\right) - 12 \, B b \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b - 12*(d*x + c)*C*b - 12*C*a*sin(d*x + c) - 12*B*b*sin(d*x + c))/d","A",0
868,1,132,0,0.333640," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b + 96 \, C b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b + 96*C*b*sin(d*x + c))/d","A",0
869,1,166,0,0.337456," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*b)/d","A",0
870,1,357,0,0.362895," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{2} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{2} - 30 \, C a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{2} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^2 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^2 - 30*C*a*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*A*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^2*tan(d*x + c))/d","A",0
871,1,306,0,0.366697," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{2} - 3 \, C b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, B a^{2} \tan\left(d x + c\right) + 96 \, A a b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^2 - 3*C*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 24*B*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 48*B*a^2*tan(d*x + c) + 96*A*a*b*tan(d*x + c))/d","A",0
872,1,207,0,0.346151," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a^{2} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{2} - 6 \, C a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 24 \, A a b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, C a^{2} \tan\left(d x + c\right) + 24 \, B a b \tan\left(d x + c\right) + 12 \, A b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a^2 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^2 - 6*C*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*B*a^2*log(sec(d*x + c) + tan(d*x + c)) + 24*A*a*b*log(sec(d*x + c) + tan(d*x + c)) + 12*C*a^2*tan(d*x + c) + 24*B*a*b*tan(d*x + c) + 12*A*b^2*tan(d*x + c))/d","A",0
873,1,189,0,0.355998," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{2} + 8 \, {\left(d x + c\right)} A a b - C b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a^{2} \sin\left(d x + c\right) + 8 \, C a b \tan\left(d x + c\right) + 4 \, B b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a^2 + 8*(d*x + c)*A*a*b - C*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a^2*sin(d*x + c) + 8*C*a*b*tan(d*x + c) + 4*B*b^2*tan(d*x + c))/d","A",0
874,1,148,0,0.363365," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 8 \, {\left(d x + c\right)} B a b + 4 \, {\left(d x + c\right)} A b^{2} + 4 \, C a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} \sin\left(d x + c\right) + 8 \, A a b \sin\left(d x + c\right) + 4 \, C b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 4*(d*x + c)*C*a^2 + 8*(d*x + c)*B*a*b + 4*(d*x + c)*A*b^2 + 4*C*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^2*sin(d*x + c) + 8*A*a*b*sin(d*x + c) + 4*C*b^2*tan(d*x + c))/d","A",0
875,1,157,0,0.354896," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b - 24 \, {\left(d x + c\right)} C a b - 12 \, {\left(d x + c\right)} B b^{2} - 6 \, C b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} \sin\left(d x + c\right) - 24 \, B a b \sin\left(d x + c\right) - 12 \, A b^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b - 24*(d*x + c)*C*a*b - 12*(d*x + c)*B*b^2 - 6*C*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*C*a^2*sin(d*x + c) - 24*B*a*b*sin(d*x + c) - 12*A*b^2*sin(d*x + c))/d","A",0
876,1,187,0,0.357096," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b + 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{2} + 96 \, {\left(d x + c\right)} C b^{2} + 192 \, C a b \sin\left(d x + c\right) + 96 \, B b^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b + 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^2 + 96*(d*x + c)*C*b^2 + 192*C*a*b*sin(d*x + c) + 96*B*b^2*sin(d*x + c))/d","A",0
877,1,233,0,0.354300," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{2} + 480 \, C b^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^2 + 480*C*b^2*sin(d*x + c))/d","A",0
878,1,565,0,0.366174," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{2} + 96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a b^{2} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B b^{3} - 5 \, C b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, C a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, B a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, A a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(160*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^2 + 96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a*b^2 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*b^3 - 5*C*b^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 90*C*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*B*a*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*A*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 360*A*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^3*tan(d*x + c))/d","A",0
879,1,445,0,0.366043," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{3} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{3} - 45 \, C a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, B a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, A a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 240 \, B a^{3} \tan\left(d x + c\right) + 720 \, A a^{2} b \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^3 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^3 - 45*C*a*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*B*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*A*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 240*B*a^3*tan(d*x + c) + 720*A*a^2*b*tan(d*x + c))/d","A",0
880,1,358,0,0.361598," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} A a^{3} + 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b^{2} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{3} - 3 \, C b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 144 \, A a^{2} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, C a^{3} \tan\left(d x + c\right) + 144 \, B a^{2} b \tan\left(d x + c\right) + 144 \, A a b^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(d*x + c)*A*a^3 + 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b^2 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^3 - 3*C*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 36*C*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*B*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*B*a^3*log(sec(d*x + c) + tan(d*x + c)) + 144*A*a^2*b*log(sec(d*x + c) + tan(d*x + c)) + 48*C*a^3*tan(d*x + c) + 144*B*a^2*b*tan(d*x + c) + 144*A*a*b^2*tan(d*x + c))/d","A",0
881,1,280,0,0.362347," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{3} + 36 \, {\left(d x + c\right)} A a^{2} b + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{3} - 9 \, C a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, B a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, A a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 36 \, C a^{2} b \tan\left(d x + c\right) + 36 \, B a b^{2} \tan\left(d x + c\right) + 12 \, A b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*B*a^3 + 36*(d*x + c)*A*a^2*b + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^3 - 9*C*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*B*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*A*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 36*C*a^2*b*tan(d*x + c) + 36*B*a*b^2*tan(d*x + c) + 12*A*b^3*tan(d*x + c))/d","A",0
882,1,243,0,0.364104," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 4 \, {\left(d x + c\right)} C a^{3} + 12 \, {\left(d x + c\right)} B a^{2} b + 12 \, {\left(d x + c\right)} A a b^{2} - C b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{3} \sin\left(d x + c\right) + 12 \, A a^{2} b \sin\left(d x + c\right) + 12 \, C a b^{2} \tan\left(d x + c\right) + 4 \, B b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 4*(d*x + c)*C*a^3 + 12*(d*x + c)*B*a^2*b + 12*(d*x + c)*A*a*b^2 - C*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^3*sin(d*x + c) + 12*A*a^2*b*sin(d*x + c) + 12*C*a*b^2*tan(d*x + c) + 4*B*b^3*tan(d*x + c))/d","A",0
883,1,216,0,0.365527," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b - 36 \, {\left(d x + c\right)} C a^{2} b - 36 \, {\left(d x + c\right)} B a b^{2} - 12 \, {\left(d x + c\right)} A b^{3} - 18 \, C a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, B b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{3} \sin\left(d x + c\right) - 36 \, B a^{2} b \sin\left(d x + c\right) - 36 \, A a b^{2} \sin\left(d x + c\right) - 12 \, C b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b - 36*(d*x + c)*C*a^2*b - 36*(d*x + c)*B*a*b^2 - 12*(d*x + c)*A*b^3 - 18*C*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*B*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*C*a^3*sin(d*x + c) - 36*B*a^2*b*sin(d*x + c) - 36*A*a*b^2*sin(d*x + c) - 12*C*b^3*tan(d*x + c))/d","A",0
884,1,246,0,0.362813," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{2} + 288 \, {\left(d x + c\right)} C a b^{2} + 96 \, {\left(d x + c\right)} B b^{3} + 48 \, C b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 288 \, C a^{2} b \sin\left(d x + c\right) + 288 \, B a b^{2} \sin\left(d x + c\right) + 96 \, A b^{3} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 96*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^2 + 288*(d*x + c)*C*a*b^2 + 96*(d*x + c)*B*b^3 + 48*C*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 288*C*a^2*b*sin(d*x + c) + 288*B*a*b^2*sin(d*x + c) + 96*A*b^3*sin(d*x + c))/d","A",0
885,1,288,0,0.346714," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} b + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{2} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{3} + 480 \, {\left(d x + c\right)} C b^{3} + 1440 \, C a b^{2} \sin\left(d x + c\right) + 480 \, B b^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2*b + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^2 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^3 + 480*(d*x + c)*C*b^3 + 1440*C*a*b^2*sin(d*x + c) + 480*B*b^3*sin(d*x + c))/d","A",0
886,1,360,0,0.363771," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} b - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b + 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{2} + 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{2} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{3} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} - 960 \, C b^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2*b - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2*b + 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b^2 + 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^2 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^3 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^3 - 960*C*b^3*sin(d*x + c))/d","A",0
887,1,746,0,0.377397," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{1120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 4480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} b + 6720 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 1344 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{2} b^{2} + 896 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a b^{3} + 224 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A b^{4} + 96 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} C b^{4} - 140 \, C a b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 35 \, B b^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, C a^{3} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 1260 \, B a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3360 \, A a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3360 \, A a^{4} \tan\left(d x + c\right)}{3360 \, d}"," ",0,"1/3360*(1120*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 4480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3*b + 6720*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b^2 + 1344*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^2*b^2 + 896*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a*b^3 + 224*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*b^4 + 96*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*C*b^4 - 140*C*a*b^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 35*B*b^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 840*C*a^3*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 1260*B*a^2*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*A*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3360*A*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 3360*A*a^4*tan(d*x + c))/d","A",0
888,1,653,0,0.376423," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} b + 960 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b^{2} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{3} + 128 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a b^{3} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B b^{4} - 5 \, C b^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 480 \, B a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 720 \, A a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 480 \, B a^{4} \tan\left(d x + c\right) + 1920 \, A a^{3} b \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3*b + 960*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b^2 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^3 + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a*b^3 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*b^4 - 5*C*b^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 180*C*a^2*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*A*b^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 480*B*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 720*A*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 480*B*a^4*tan(d*x + c) + 1920*A*a^3*b*tan(d*x + c))/d","A",0
889,1,497,0,0.348433," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(d x + c\right)} A a^{4} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b^{2} + 320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{3} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{4} + 16 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C b^{4} - 60 \, C a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, C a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, B a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, A a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, B a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 960 \, A a^{3} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 240 \, C a^{4} \tan\left(d x + c\right) + 960 \, B a^{3} b \tan\left(d x + c\right) + 1440 \, A a^{2} b^{2} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(240*(d*x + c)*A*a^4 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b^2 + 320*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^3 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^4 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*b^4 - 60*C*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*b^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 240*C*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 360*B*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 240*A*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*B*a^4*log(sec(d*x + c) + tan(d*x + c)) + 960*A*a^3*b*log(sec(d*x + c) + tan(d*x + c)) + 240*C*a^4*tan(d*x + c) + 960*B*a^3*b*tan(d*x + c) + 1440*A*a^2*b^2*tan(d*x + c))/d","A",0
890,1,431,0,0.362358," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} B a^{4} + 192 \, {\left(d x + c\right)} A a^{3} b + 64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{4} - 3 \, C b^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, C a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 48 \, B a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, B a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, A a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{4} \sin\left(d x + c\right) + 192 \, C a^{3} b \tan\left(d x + c\right) + 288 \, B a^{2} b^{2} \tan\left(d x + c\right) + 192 \, A a b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(d*x + c)*B*a^4 + 192*(d*x + c)*A*a^3*b + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^4 - 3*C*b^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 72*C*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 48*B*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*B*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 144*A*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^4*sin(d*x + c) + 192*C*a^3*b*tan(d*x + c) + 288*B*a^2*b^2*tan(d*x + c) + 192*A*a*b^3*tan(d*x + c))/d","A",0
891,1,335,0,0.358539," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 12 \, {\left(d x + c\right)} C a^{4} + 48 \, {\left(d x + c\right)} B a^{3} b + 72 \, {\left(d x + c\right)} A a^{2} b^{2} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{4} - 12 \, C a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{4} \sin\left(d x + c\right) + 48 \, A a^{3} b \sin\left(d x + c\right) + 72 \, C a^{2} b^{2} \tan\left(d x + c\right) + 48 \, B a b^{3} \tan\left(d x + c\right) + 12 \, A b^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 12*(d*x + c)*C*a^4 + 48*(d*x + c)*B*a^3*b + 72*(d*x + c)*A*a^2*b^2 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^4 - 12*C*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*A*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*B*a^4*sin(d*x + c) + 48*A*a^3*b*sin(d*x + c) + 72*C*a^2*b^2*tan(d*x + c) + 48*B*a*b^3*tan(d*x + c) + 12*A*b^4*tan(d*x + c))/d","A",0
892,1,311,0,0.354321," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 48 \, {\left(d x + c\right)} C a^{3} b - 72 \, {\left(d x + c\right)} B a^{2} b^{2} - 48 \, {\left(d x + c\right)} A a b^{3} + 3 \, C b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, A b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} \sin\left(d x + c\right) - 48 \, B a^{3} b \sin\left(d x + c\right) - 72 \, A a^{2} b^{2} \sin\left(d x + c\right) - 48 \, C a b^{3} \tan\left(d x + c\right) - 12 \, B b^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3*b - 48*(d*x + c)*C*a^3*b - 72*(d*x + c)*B*a^2*b^2 - 48*(d*x + c)*A*a*b^3 + 3*C*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*C*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 24*B*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*A*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*C*a^4*sin(d*x + c) - 48*B*a^3*b*sin(d*x + c) - 72*A*a^2*b^2*sin(d*x + c) - 48*C*a*b^3*tan(d*x + c) - 12*B*b^4*tan(d*x + c))/d","A",0
893,1,305,0,0.360104," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} b + 96 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} b + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b^{2} + 576 \, {\left(d x + c\right)} C a^{2} b^{2} + 384 \, {\left(d x + c\right)} B a b^{3} + 96 \, {\left(d x + c\right)} A b^{4} + 192 \, C a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 384 \, C a^{3} b \sin\left(d x + c\right) + 576 \, B a^{2} b^{2} \sin\left(d x + c\right) + 384 \, A a b^{3} \sin\left(d x + c\right) + 96 \, C b^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3*b + 96*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3*b + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b^2 + 576*(d*x + c)*C*a^2*b^2 + 384*(d*x + c)*B*a*b^3 + 96*(d*x + c)*A*b^4 + 192*C*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*B*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 384*C*a^3*b*sin(d*x + c) + 576*B*a^2*b^2*sin(d*x + c) + 384*A*a*b^3*sin(d*x + c) + 96*C*b^4*tan(d*x + c))/d","A",0
894,1,347,0,0.362632," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 60 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} b + 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} b^{2} + 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b^{2} + 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} + 1920 \, {\left(d x + c\right)} C a b^{3} + 480 \, {\left(d x + c\right)} B b^{4} + 240 \, C b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2880 \, C a^{2} b^{2} \sin\left(d x + c\right) + 1920 \, B a b^{3} \sin\left(d x + c\right) + 480 \, A b^{4} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 60*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3*b - 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3*b + 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3*b - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2*b^2 + 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b^2 + 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^3 + 1920*(d*x + c)*C*a*b^3 + 480*(d*x + c)*B*b^4 + 240*C*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2880*C*a^2*b^2*sin(d*x + c) + 1920*B*a*b^3*sin(d*x + c) + 480*A*b^4*sin(d*x + c))/d","A",0
895,1,415,0,0.357574," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 256 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} b - 120 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} b + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} b - 180 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b^{2} + 1920 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} b^{2} - 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b^{2} + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{3} - 960 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{3} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{4} - 960 \, {\left(d x + c\right)} C b^{4} - 3840 \, C a b^{3} \sin\left(d x + c\right) - 960 \, B b^{4} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3*b - 120*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3*b + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3*b - 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2*b^2 + 1920*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2*b^2 - 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b^2 + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^3 - 960*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^3 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^4 - 960*(d*x + c)*C*b^4 - 3840*C*a*b^3*sin(d*x + c) - 960*B*b^4*sin(d*x + c))/d","A",0
896,1,498,0,0.356569," ","integrate(cos(d*x+c)^7*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} A a^{4} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} + 140 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 1792 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} b - 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b - 2688 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{2} b^{2} - 1260 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b^{2} + 13440 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b^{2} - 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} + 8960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{3} - 6720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} + 2240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{4} - 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{4} - 6720 \, C b^{4} \sin\left(d x + c\right)}{6720 \, d}"," ",0,"-1/6720*(192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*A*a^4 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^4 - 448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 140*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3*b - 1792*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3*b - 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3*b - 2688*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^2*b^2 - 1260*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2*b^2 + 13440*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b^2 - 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b^3 + 8960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^3 - 6720*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^3 + 2240*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^4 - 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^4 - 6720*C*b^4*sin(d*x + c))/d","A",0
897,1,320,0,0.363903," ","integrate((a+b*sec(d*x+c))^3*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{48 \, {\left(d x + c\right)} C a^{5} - 48 \, {\left(d x + c\right)} B a^{4} b - 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a b^{4} - 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{5} + 3 \, C b^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{2} b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a^{4} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 192 \, B a^{3} b^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 96 \, C a^{3} b^{2} \tan\left(d x + c\right) - 288 \, B a^{2} b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"-1/48*(48*(d*x + c)*C*a^5 - 48*(d*x + c)*B*a^4*b - 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a*b^4 - 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^5 + 3*C*b^5*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 24*C*a^2*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*B*a*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 144*C*a^4*b*log(sec(d*x + c) + tan(d*x + c)) - 192*B*a^3*b^2*log(sec(d*x + c) + tan(d*x + c)) + 96*C*a^3*b^2*tan(d*x + c) - 288*B*a^2*b^3*tan(d*x + c))/d","A",0
898,1,204,0,0.353413," ","integrate((a+b*sec(d*x+c))^2*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{12 \, {\left(d x + c\right)} C a^{4} - 12 \, {\left(d x + c\right)} B a^{3} b - 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C b^{4} + 6 \, C a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3 \, B b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 36 \, B a^{2} b^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 36 \, B a b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(12*(d*x + c)*C*a^4 - 12*(d*x + c)*B*a^3*b - 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*b^4 + 6*C*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 3*B*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*b*log(sec(d*x + c) + tan(d*x + c)) - 36*B*a^2*b^2*log(sec(d*x + c) + tan(d*x + c)) - 36*B*a*b^3*tan(d*x + c))/d","A",0
899,1,142,0,0.351524," ","integrate((a+b*sec(d*x+c))*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c\right)} C a^{3} - 4 \, {\left(d x + c\right)} B a^{2} b + C b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 8 \, B a b^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 4 \, C a b^{2} \tan\left(d x + c\right) - 4 \, B b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(4*(d*x + c)*C*a^3 - 4*(d*x + c)*B*a^2*b + C*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*C*a^2*b*log(sec(d*x + c) + tan(d*x + c)) - 8*B*a*b^2*log(sec(d*x + c) + tan(d*x + c)) - 4*C*a*b^2*tan(d*x + c) - 4*B*b^3*tan(d*x + c))/d","A",0
900,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
901,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
902,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
903,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
904,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
905,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
906,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
907,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
908,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
909,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
910,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
911,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
912,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
913,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
914,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
915,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
916,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
917,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
918,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
919,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
920,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
921,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
922,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
923,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
924,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
925,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
926,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
927,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
928,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
929,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
930,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
931,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
932,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
933,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
934,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
935,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
936,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
937,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
938,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
939,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
940,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
941,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
942,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
943,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
944,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
945,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
946,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
947,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
948,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
949,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
950,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
951,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
952,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
953,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
954,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
955,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
956,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
957,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^5, x)","F",0
958,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
959,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
960,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
961,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
962,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
963,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
964,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
965,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
966,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
967,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
968,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
969,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
970,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
971,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
972,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
973,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
974,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
975,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
976,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*sqrt(b*sec(d*x + c) + a), x)","F",0
977,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)/sqrt(b*sec(d*x + c) + a), x)","F",0
978,-1,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
979,-1,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
980,-1,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
981,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
982,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
983,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
984,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
985,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
986,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
987,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
988,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
989,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
990,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
991,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
992,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
993,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
994,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
995,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
996,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
997,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
998,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
999,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1000,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1001,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1002,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1003,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1004,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1005,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1006,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1007,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1008,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1009,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1010,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1011,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1012,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1013,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1014,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
1015,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1016,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1017,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1018,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
1019,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1020,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1022,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1023,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1024,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1027,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1030,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1031,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1032,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1033,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1034,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1035,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
1036,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
1037,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
1038,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
1039,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
1040,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
1041,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
1042,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
1043,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
1044,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
1045,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1046,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
1047,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
1048,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
1049,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
1050,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
1051,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
1052,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1053,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1054,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1055,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1056,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1057,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
1058,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1059,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1060,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1061,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1062,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1063,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1064,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
1067,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1068,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1069,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1070,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
1071,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(1/3), x)","F",0
1072,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
1073,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
1074,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^m*(a*b*B-a^2*C+b^2*B*sec(d*x+c)+b^2*C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C b^{2} \sec\left(d x + c\right)^{2} + B b^{2} \sec\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*b^2*sec(d*x + c)^2 + B*b^2*sec(d*x + c) - C*a^2 + B*a*b)*(b*sec(d*x + c) + a)^m, x)","F",0
1075,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(9/2), x)","F",0
1076,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(7/2), x)","F",0
1077,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2), x)","F",0
1078,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2), x)","F",0
1079,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c)), x)","F",0
1080,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/sqrt(cos(d*x + c)), x)","F",0
1081,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/cos(d*x + c)^(3/2), x)","F",0
1082,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/cos(d*x + c)^(5/2), x)","F",0
1083,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1084,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1085,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1086,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1087,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1088,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1089,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1090,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1091,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1092,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
1093,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
1094,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1095,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1096,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
1097,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1098,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1099,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1100,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1101,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1103,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
1104,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*(a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
1105,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1106,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1107,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
1108,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
1109,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
1110,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1111,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1112,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1113,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1115,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1116,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
1117,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1118,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1119,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1120,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1121,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1122,0,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
1123,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1124,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1125,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1127,1,507,0,0.673186," ","integrate(cos(d*x+c)^(9/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(1890 \, \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 420 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 252 \, \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 1890 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 420 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 252 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 45 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 252 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 420 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1890 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 84 \, \sqrt{2} {\left(5 \, {\left(6 \, \sin\left(2 \, d x + 2 \, c\right) + \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - {\left(30 \, \cos\left(2 \, d x + 2 \, c\right) + 5 \, \cos\left(d x + c\right) + 6\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 5 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 30 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(1890*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 420*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 252*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 45*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 1890*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 420*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 252*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 45*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*sin(9/2*d*x + 9/2*c) + 45*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 252*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 420*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1890*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) - 84*sqrt(2)*(5*(6*sin(2*d*x + 2*c) + sin(d*x + c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - (30*cos(2*d*x + 2*c) + 5*cos(d*x + c) + 6)*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 5*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 30*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a))/d","B",0
1128,1,387,0,0.686486," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(105 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 35 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 105 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 35 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 7 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 10 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 140 \, {\left(3 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(d x + c\right) - {\left(3 \, \sqrt{2} \cos\left(d x + c\right) + 2 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(3*sqrt(2)*(105*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 35*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 7*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 105*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 35*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 7*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 10*sin(7/2*d*x + 7/2*c) + 7*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) - 140*(3*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(d*x + c) - (3*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a))/d","B",0
1129,1,231,0,0.665098," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 120 \, \sqrt{2} C \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)}{60 \, d}"," ",0,"1/60*(sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 120*sqrt(2)*C*sqrt(a)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))/d","B",0
1130,1,355,0,0.679552," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 3 \, C \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)}}{6 \, d}"," ",0,"1/6*(sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) + 3*C*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)))/d","B",0
1131,1,731,0,0.683834," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) - (4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
1132,1,1507,0,0.765791," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, A \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} - \frac{{\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{16 \, d}"," ",0,"1/16*(8*A*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)) - (12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
1133,1,2740,0,0.872742," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + (60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
1134,1,4417,0,1.096816," ","integrate((A+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + (420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(15/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(13/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(15/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(13/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
1135,1,652,0,0.714995," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{7 \, \sqrt{2} {\left(3630 \, a \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 990 \, a \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 429 \, a \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 165 \, a \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 3630 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 990 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 429 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 165 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 55 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 165 \, a \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 429 \, a \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 990 \, a \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3630 \, a \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 44 \, \sqrt{2} {\left(175 \, a \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 5 \, {\left(35 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 126 \, a \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 175 \, a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1470 \, a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{36960 \, d}"," ",0,"1/36960*(7*sqrt(2)*(3630*a*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 990*a*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 429*a*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 165*a*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 55*a*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 3630*a*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 990*a*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 429*a*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 165*a*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 55*a*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 30*a*sin(11/2*d*x + 11/2*c) + 55*a*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 165*a*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 429*a*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 990*a*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3630*a*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) - 44*sqrt(2)*(175*a*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 5*(35*a*cos(2*d*x + 2*c) + 6*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 126*a*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 175*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1470*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1136,1,544,0,0.691970," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3780 \, a \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1050 \, a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 378 \, a \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 3780 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 1050 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 378 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 135 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 378 \, a \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1050 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 3780 \, a \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 504 \, {\left(10 \, \sqrt{2} a \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 10 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(10 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(3780*a*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 1050*a*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 378*a*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 135*a*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 3780*a*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 1050*a*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 378*a*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 135*a*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a*sin(9/2*d*x + 9/2*c) + 135*a*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 378*a*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1050*a*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 3780*a*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) - 504*(10*sqrt(2)*a*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 5*sqrt(2)*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 10*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (10*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1137,1,368,0,0.677745," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 280 \, {\left(\sqrt{2} a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 280*(sqrt(2)*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 9*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1138,1,694,0,0.711266," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 10 \, {\left(4 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} C \sqrt{a}}{20 \, d}"," ",0,"1/20*(sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 10*(4*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*C*sqrt(a))/d","B",0
1139,1,1354,0,0.788580," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} - \frac{3 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 2 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 6 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(4*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) - 3*(2*sqrt(2)*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 6*sqrt(2)*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 5*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 2*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/2*d*x + 7/2*c) - 6*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/2*d*x + 5/2*c) + 2*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
1140,1,2520,0,0.842283," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} - \frac{{\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1}}{16 \, d}"," ",0,"1/16*(4*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) - (56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1))/d","B",0
1141,1,3506,0,0.878941," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"1/96*(24*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
1142,1,5761,0,1.160706," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{16 \, {\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1} + \frac{{\left(300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{256 \, d}"," ",0,"-1/256*(16*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
1143,1,7235,0,1.718566," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{80 \, {\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(7980 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2660 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 38304 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12160 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 45400 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 45400 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12160 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 38304 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2660 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 7980 \, {\left(\sqrt{2} a \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 1995 \, {\left(a \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(5 \, a \cos\left(8 \, d x + 8 \, c\right) + 10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a \cos\left(6 \, d x + 6 \, c\right) + 10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right) + 5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, a \cos\left(2 \, d x + 2 \, c\right) + 10 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7980 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2660 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 38304 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12160 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 45400 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 45400 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12160 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 38304 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2660 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7980 \, {\left(\sqrt{2} a \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(5 \, \cos\left(8 \, d x + 8 \, c\right) + 10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + \cos\left(10 \, d x + 10 \, c\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 25 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 100 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 100 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + \sin\left(10 \, d x + 10 \, c\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 25 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 100 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{7680 \, d}"," ",0,"-1/7680*(80*(132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + (7980*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2660*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 38304*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12160*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 45400*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 45400*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12160*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 38304*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2660*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 7980*(sqrt(2)*a*sin(10*d*x + 10*c) + 5*sqrt(2)*a*sin(8*d*x + 8*c) + 10*sqrt(2)*a*sin(6*d*x + 6*c) + 10*sqrt(2)*a*sin(4*d*x + 4*c) + 5*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 1995*(a*cos(10*d*x + 10*c)^2 + 25*a*cos(8*d*x + 8*c)^2 + 100*a*cos(6*d*x + 6*c)^2 + 100*a*cos(4*d*x + 4*c)^2 + 25*a*cos(2*d*x + 2*c)^2 + a*sin(10*d*x + 10*c)^2 + 25*a*sin(8*d*x + 8*c)^2 + 100*a*sin(6*d*x + 6*c)^2 + 100*a*sin(4*d*x + 4*c)^2 + 100*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a*sin(2*d*x + 2*c)^2 + 2*(5*a*cos(8*d*x + 8*c) + 10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(10*d*x + 10*c) + 10*(10*a*cos(6*d*x + 6*c) + 10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 20*(10*a*cos(4*d*x + 4*c) + 5*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 20*(5*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 10*a*cos(2*d*x + 2*c) + 10*(a*sin(8*d*x + 8*c) + 2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a*sin(6*d*x + 6*c) + 2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7980*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2660*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 38304*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12160*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 45400*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 45400*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12160*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 38304*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2660*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7980*(sqrt(2)*a*cos(10*d*x + 10*c) + 5*sqrt(2)*a*cos(8*d*x + 8*c) + 10*sqrt(2)*a*cos(6*d*x + 6*c) + 10*sqrt(2)*a*cos(4*d*x + 4*c) + 5*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(5*cos(8*d*x + 8*c) + 10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + cos(10*d*x + 10*c)^2 + 10*(10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 25*cos(8*d*x + 8*c)^2 + 20*(10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 100*cos(6*d*x + 6*c)^2 + 20*(5*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 100*cos(4*d*x + 4*c)^2 + 25*cos(2*d*x + 2*c)^2 + 10*(sin(8*d*x + 8*c) + 2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + sin(10*d*x + 10*c)^2 + 50*(2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 25*sin(8*d*x + 8*c)^2 + 100*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 100*sin(6*d*x + 6*c)^2 + 100*sin(4*d*x + 4*c)^2 + 100*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*sin(2*d*x + 2*c)^2 + 10*cos(2*d*x + 2*c) + 1))/d","B",0
1144,1,852,0,0.720677," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3783780 \, a^{2} \cos\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 1066065 \, a^{2} \cos\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 459459 \, a^{2} \cos\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 193050 \, a^{2} \cos\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 70070 \, a^{2} \cos\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \cos\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 3783780 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 1066065 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 459459 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 193050 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 70070 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 20475 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 6930 \, a^{2} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \sin\left(\frac{11}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 70070 \, a^{2} \sin\left(\frac{9}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 193050 \, a^{2} \sin\left(\frac{7}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 459459 \, a^{2} \sin\left(\frac{5}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 1066065 \, a^{2} \sin\left(\frac{3}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 3783780 \, a^{2} \sin\left(\frac{1}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 1144 \, \sqrt{2} {\left(225 \, a^{2} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 378 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4095 \, a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 63 \, {\left(65 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7 \, {\left(585 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 54 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 5 \, a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2882880 \, d}"," ",0,"1/2882880*(sqrt(2)*(3783780*a^2*cos(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 1066065*a^2*cos(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 459459*a^2*cos(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 193050*a^2*cos(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 70070*a^2*cos(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 20475*a^2*cos(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) - 3783780*a^2*cos(13/2*d*x + 13/2*c)*sin(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 1066065*a^2*cos(13/2*d*x + 13/2*c)*sin(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 459459*a^2*cos(13/2*d*x + 13/2*c)*sin(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 193050*a^2*cos(13/2*d*x + 13/2*c)*sin(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 70070*a^2*cos(13/2*d*x + 13/2*c)*sin(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 20475*a^2*cos(13/2*d*x + 13/2*c)*sin(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 6930*a^2*sin(13/2*d*x + 13/2*c) + 20475*a^2*sin(11/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 70070*a^2*sin(9/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 193050*a^2*sin(7/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 459459*a^2*sin(5/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 1066065*a^2*sin(3/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 3783780*a^2*sin(1/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))))*A*sqrt(a) + 1144*sqrt(2)*(225*a^2*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 378*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2100*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4095*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 63*(65*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7*(585*a^2*cos(4*d*x + 4*c) + 54*a^2*cos(2*d*x + 2*c) + 5*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1145,1,695,0,0.696356," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(31878 \, a^{2} \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 8778 \, a^{2} \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 3465 \, a^{2} \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1287 \, a^{2} \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 31878 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 8778 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 3465 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1287 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 385 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 126 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1287 \, a^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3465 \, a^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 8778 \, a^{2} \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 31878 \, a^{2} \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 132 \, \sqrt{2} {\left(77 \, a^{2} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 42 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 77 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 630 \, a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(77 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 6 \, a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{22176 \, d}"," ",0,"1/22176*(sqrt(2)*(31878*a^2*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 8778*a^2*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 3465*a^2*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 1287*a^2*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 385*a^2*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 31878*a^2*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 8778*a^2*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 3465*a^2*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1287*a^2*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 385*a^2*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 126*a^2*sin(11/2*d*x + 11/2*c) + 385*a^2*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1287*a^2*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3465*a^2*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 8778*a^2*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 31878*a^2*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) - 132*sqrt(2)*(77*a^2*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 42*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 77*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 630*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (77*a^2*cos(2*d*x + 2*c) + 6*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1146,1,580,0,0.677682," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 168 \, {\left(75 \, \sqrt{2} a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) - 168*(75*sqrt(2)*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 25*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(25*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1147,1,849,0,0.779697," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 28 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 30 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} C \sqrt{a}}{168 \, d}"," ",0,"1/168*(sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) + 28*(2*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 30*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*C*sqrt(a))/d","B",0
1148,1,8175,0,1.086068," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{42 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} - \frac{5 \, {\left(1449 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} \sin\left(2 \, d x + 2 \, c\right) - 1260 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1449 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(25 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 198 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 69 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 98 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, {\left(50 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 50 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(50 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 21 \, {\left(60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 7 \, {\left(9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} + 138 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 50 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 105 \, {\left(12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 252 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 63 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1260 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{1260 \, d}"," ",0,"1/1260*(42*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) - 5*(1449*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^3*sin(2*d*x + 2*c) - 1260*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 1449*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^3 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 5*(5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (25*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 198*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*cos(2*d*x + 2*c)^2 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 69*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + (25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 5*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c)^2 - 35*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 135*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) - 98*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 390*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(7/2*d*x + 7/2*c) + 21*(50*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) + 50*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 120*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 10*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (50*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 69*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c) - 21*(60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) + 12*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 35*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(13/2*d*x + 13/2*c) + 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(11/2*d*x + 11/2*c) + 7*(9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 4*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(9/2*d*x + 9/2*c) - 390*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/2*d*x + 7/2*c) - 21*(69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 69*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*cos(2*d*x + 2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*sin(2*d*x + 2*c)^2 + 12*sqrt(2)*a^2 + 138*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - sqrt(2)*a^2*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 - 50*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 24*sqrt(2)*a^2)*cos(2*d*x + 2*c) - 10*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c) + 105*(12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c) - 252*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c) - 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 63*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1260*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + cos(1/2*d*x + 1/2*c)^2 + 2*(cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c) + sin(1/2*d*x + 1/2*c)^2))/d","B",0
1149,1,3421,0,4.126307," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(30 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 30 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - \frac{3 \, {\left(88 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 56 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 44 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(22 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 14 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 38 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(11 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 44 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 28 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{48 \, d}"," ",0,"1/48*(4*sqrt(2)*(30*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 30*a^2*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*a^2*sin(3/2*d*x + 3/2*c) + 30*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) - 3*(88*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 56*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 44*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 2*(22*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) - 14*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 38*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 4*(11*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c) - 7*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c) + 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 44*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) + 28*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c) + 8*(7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
1150,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,1,6687,0,4.407933," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(88 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 56 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 44 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(22 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 14 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 38 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(11 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 44 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 28 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(88*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 56*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 44*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 2*(22*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) - 14*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 38*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 4*(11*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c) - 7*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c) + 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 44*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) + 28*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c) + 8*(7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + (1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
1152,1,8852,0,1.823038," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\frac{80 \, {\left(300 \, \sqrt{2} a^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(6 \, d x + 6 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 28 \, {\left(\sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 300 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{11}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(7 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 114 \, \sqrt{2} a^{2} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 114 \, \sqrt{2} a^{2} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 456 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 456 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(7 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 75 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 9 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2} + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 6 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 28 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 300 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 114 \, \sqrt{2} a^{2} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 114 \, \sqrt{2} a^{2} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 75 \, \sqrt{2} a^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 456 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 456 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 75 \, \sqrt{2} a^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 300 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{\cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 3 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 6 \, \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 9 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(6 \, d x + 6 \, c\right) + 1} - \frac{{\left(16980 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 5660 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 81504 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8320 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 86440 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 86440 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8320 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 81504 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 5660 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16980 \, {\left(\sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 4245 \, {\left(a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 25 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(5 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 10 \, {\left(10 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 20 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 20 \, {\left(5 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(a^{2} \sin\left(8 \, d x + 8 \, c\right) + 2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 50 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 100 \, {\left(2 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16980 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 5660 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 81504 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8320 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 86440 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 86440 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8320 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 81504 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 5660 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16980 \, {\left(\sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(5 \, \cos\left(8 \, d x + 8 \, c\right) + 10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + \cos\left(10 \, d x + 10 \, c\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, d x + 6 \, c\right) + 10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 25 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, d x + 4 \, c\right) + 5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 100 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 100 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 25 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 10 \, {\left(\sin\left(8 \, d x + 8 \, c\right) + 2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + \sin\left(10 \, d x + 10 \, c\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 25 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 100 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 100 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 25 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 10 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{7680 \, d}"," ",0,"1/7680*(80*(300*sqrt(2)*a^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(6*d*x + 6*c) - 28*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 28*(sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) - sqrt(2)*a^2*sin(3/2*d*x + 3/2*c))*cos(6*d*x + 6*c) - 300*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 3*sqrt(2)*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(11/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(7*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 114*sqrt(2)*a^2*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 114*sqrt(2)*a^2*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 75*sqrt(2)*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 456*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 456*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(7*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 75*sqrt(2)*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 75*(a^2*cos(6*d*x + 6*c)^2 + 9*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 9*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a^2*sin(6*d*x + 6*c)^2 + 9*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*a^2*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*a^2*cos(6*d*x + 6*c) + a^2 + 6*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*cos(6*d*x + 6*c) + a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 6*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 28*(sqrt(2)*a^2*cos(9/2*d*x + 9/2*c) - sqrt(2)*a^2*cos(3/2*d*x + 3/2*c))*sin(6*d*x + 6*c) + 300*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 3*sqrt(2)*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*sin(11/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(7*sqrt(2)*a^2*cos(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 114*sqrt(2)*a^2*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 114*sqrt(2)*a^2*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 75*sqrt(2)*a^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 456*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 3*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 456*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 3*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(7*sqrt(2)*a^2*cos(9/2*d*x + 9/2*c) - 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 75*sqrt(2)*a^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 300*(sqrt(2)*a^2*cos(6*d*x + 6*c) + sqrt(2)*a^2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(cos(6*d*x + 6*c)^2 + 6*(cos(6*d*x + 6*c) + 3*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*(cos(6*d*x + 6*c) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(6*d*x + 6*c)^2 + 6*(sin(6*d*x + 6*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 6*sin(6*d*x + 6*c)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 9*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(6*d*x + 6*c) + 1) - (16980*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 5660*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 81504*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8320*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 86440*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 86440*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8320*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 81504*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 5660*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16980*(sqrt(2)*a^2*sin(10*d*x + 10*c) + 5*sqrt(2)*a^2*sin(8*d*x + 8*c) + 10*sqrt(2)*a^2*sin(6*d*x + 6*c) + 10*sqrt(2)*a^2*sin(4*d*x + 4*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 4245*(a^2*cos(10*d*x + 10*c)^2 + 25*a^2*cos(8*d*x + 8*c)^2 + 100*a^2*cos(6*d*x + 6*c)^2 + 100*a^2*cos(4*d*x + 4*c)^2 + 25*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(10*d*x + 10*c)^2 + 25*a^2*sin(8*d*x + 8*c)^2 + 100*a^2*sin(6*d*x + 6*c)^2 + 100*a^2*sin(4*d*x + 4*c)^2 + 100*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*a^2*sin(2*d*x + 2*c)^2 + 10*a^2*cos(2*d*x + 2*c) + a^2 + 2*(5*a^2*cos(8*d*x + 8*c) + 10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 10*(10*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 20*(10*a^2*cos(4*d*x + 4*c) + 5*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 20*(5*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 10*(a^2*sin(8*d*x + 8*c) + 2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 50*(2*a^2*sin(6*d*x + 6*c) + 2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 100*(2*a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16980*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 5660*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 81504*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8320*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 86440*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 86440*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8320*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 81504*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 5660*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16980*(sqrt(2)*a^2*cos(10*d*x + 10*c) + 5*sqrt(2)*a^2*cos(8*d*x + 8*c) + 10*sqrt(2)*a^2*cos(6*d*x + 6*c) + 10*sqrt(2)*a^2*cos(4*d*x + 4*c) + 5*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(5*cos(8*d*x + 8*c) + 10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + cos(10*d*x + 10*c)^2 + 10*(10*cos(6*d*x + 6*c) + 10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 25*cos(8*d*x + 8*c)^2 + 20*(10*cos(4*d*x + 4*c) + 5*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 100*cos(6*d*x + 6*c)^2 + 20*(5*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 100*cos(4*d*x + 4*c)^2 + 25*cos(2*d*x + 2*c)^2 + 10*(sin(8*d*x + 8*c) + 2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + sin(10*d*x + 10*c)^2 + 50*(2*sin(6*d*x + 6*c) + 2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 25*sin(8*d*x + 8*c)^2 + 100*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 100*sin(6*d*x + 6*c)^2 + 100*sin(4*d*x + 4*c)^2 + 100*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 25*sin(2*d*x + 2*c)^2 + 10*cos(2*d*x + 2*c) + 1))/d","B",0
1153,1,11081,0,2.980737," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1956 \, {\left(\sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 489 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2060 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6204 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 652 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1956 \, {\left(\sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(12180 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{23}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4060 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{21}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 70644 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 22620 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 147592 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 37800 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 37800 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 147592 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 22620 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 70644 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4060 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12180 \, {\left(\sqrt{2} a^{2} \sin\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3045 \, {\left(a^{2} \cos\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \cos\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(12 \, d x + 12 \, c\right)^{2} + 36 \, a^{2} \sin\left(10 \, d x + 10 \, c\right)^{2} + 225 \, a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 400 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(6 \, a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 40 \, {\left(15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 30 \, {\left(6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(6 \, a^{2} \sin\left(10 \, d x + 10 \, c\right) + 15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + 12 \, {\left(15 \, a^{2} \sin\left(8 \, d x + 8 \, c\right) + 20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 30 \, {\left(20 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 120 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 12180 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{23}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4060 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{21}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 70644 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{19}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 22620 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{17}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 147592 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 37800 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 37800 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 147592 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 22620 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 70644 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4060 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12180 \, {\left(\sqrt{2} a^{2} \cos\left(12 \, d x + 12 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(10 \, d x + 10 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(8 \, d x + 8 \, c\right) + 20 \, \sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 15 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(6 \, \cos\left(10 \, d x + 10 \, c\right) + 15 \, \cos\left(8 \, d x + 8 \, c\right) + 20 \, \cos\left(6 \, d x + 6 \, c\right) + 15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(12 \, d x + 12 \, c\right) + \cos\left(12 \, d x + 12 \, c\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, d x + 8 \, c\right) + 20 \, \cos\left(6 \, d x + 6 \, c\right) + 15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(10 \, d x + 10 \, c\right) + 36 \, \cos\left(10 \, d x + 10 \, c\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, d x + 6 \, c\right) + 15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 225 \, \cos\left(8 \, d x + 8 \, c\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 400 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 225 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, d x + 10 \, c\right) + 15 \, \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(12 \, d x + 12 \, c\right) + \sin\left(12 \, d x + 12 \, c\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, d x + 8 \, c\right) + 20 \, \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(10 \, d x + 10 \, c\right) + 36 \, \sin\left(10 \, d x + 10 \, c\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, d x + 6 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 225 \, \sin\left(8 \, d x + 8 \, c\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 400 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 225 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 180 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{6144 \, d}"," ",0,"-1/6144*(8*(1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1956*(sqrt(2)*a^2*sin(8*d*x + 8*c) + 4*sqrt(2)*a^2*sin(6*d*x + 6*c) + 6*sqrt(2)*a^2*sin(4*d*x + 4*c) + 4*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 489*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2060*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6204*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 652*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1956*(sqrt(2)*a^2*cos(8*d*x + 8*c) + 4*sqrt(2)*a^2*cos(6*d*x + 6*c) + 6*sqrt(2)*a^2*cos(4*d*x + 4*c) + 4*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1) + (12180*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(23/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4060*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(21/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 70644*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 22620*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 147592*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 37800*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 37800*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 147592*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 22620*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 70644*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4060*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12180*(sqrt(2)*a^2*sin(12*d*x + 12*c) + 6*sqrt(2)*a^2*sin(10*d*x + 10*c) + 15*sqrt(2)*a^2*sin(8*d*x + 8*c) + 20*sqrt(2)*a^2*sin(6*d*x + 6*c) + 15*sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3045*(a^2*cos(12*d*x + 12*c)^2 + 36*a^2*cos(10*d*x + 10*c)^2 + 225*a^2*cos(8*d*x + 8*c)^2 + 400*a^2*cos(6*d*x + 6*c)^2 + 225*a^2*cos(4*d*x + 4*c)^2 + 36*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(12*d*x + 12*c)^2 + 36*a^2*sin(10*d*x + 10*c)^2 + 225*a^2*sin(8*d*x + 8*c)^2 + 400*a^2*sin(6*d*x + 6*c)^2 + 225*a^2*sin(4*d*x + 4*c)^2 + 180*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*a^2*sin(2*d*x + 2*c)^2 + 12*a^2*cos(2*d*x + 2*c) + a^2 + 2*(6*a^2*cos(10*d*x + 10*c) + 15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(12*d*x + 12*c) + 12*(15*a^2*cos(8*d*x + 8*c) + 20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(10*d*x + 10*c) + 30*(20*a^2*cos(6*d*x + 6*c) + 15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 40*(15*a^2*cos(4*d*x + 4*c) + 6*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 30*(6*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 2*(6*a^2*sin(10*d*x + 10*c) + 15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + 12*(15*a^2*sin(8*d*x + 8*c) + 20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 30*(20*a^2*sin(6*d*x + 6*c) + 15*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 120*(5*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 12180*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(23/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4060*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(21/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 70644*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(19/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 22620*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(17/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 147592*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 37800*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 37800*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 147592*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 22620*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 70644*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4060*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12180*(sqrt(2)*a^2*cos(12*d*x + 12*c) + 6*sqrt(2)*a^2*cos(10*d*x + 10*c) + 15*sqrt(2)*a^2*cos(8*d*x + 8*c) + 20*sqrt(2)*a^2*cos(6*d*x + 6*c) + 15*sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(6*cos(10*d*x + 10*c) + 15*cos(8*d*x + 8*c) + 20*cos(6*d*x + 6*c) + 15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(12*d*x + 12*c) + cos(12*d*x + 12*c)^2 + 12*(15*cos(8*d*x + 8*c) + 20*cos(6*d*x + 6*c) + 15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(10*d*x + 10*c) + 36*cos(10*d*x + 10*c)^2 + 30*(20*cos(6*d*x + 6*c) + 15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 225*cos(8*d*x + 8*c)^2 + 40*(15*cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 400*cos(6*d*x + 6*c)^2 + 30*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 225*cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 2*(6*sin(10*d*x + 10*c) + 15*sin(8*d*x + 8*c) + 20*sin(6*d*x + 6*c) + 15*sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(12*d*x + 12*c) + sin(12*d*x + 12*c)^2 + 12*(15*sin(8*d*x + 8*c) + 20*sin(6*d*x + 6*c) + 15*sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(10*d*x + 10*c) + 36*sin(10*d*x + 10*c)^2 + 30*(20*sin(6*d*x + 6*c) + 15*sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 225*sin(8*d*x + 8*c)^2 + 120*(5*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 400*sin(6*d*x + 6*c)^2 + 225*sin(4*d*x + 4*c)^2 + 180*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 12*cos(2*d*x + 2*c) + 1))/d","B",0
1154,1,671,0,0.713242," ","integrate(cos(d*x+c)^(7/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{2} {\left(525 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 175 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 525 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) + 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) - 30 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 525 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{140 \, {\left(3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{\sqrt{a}}}{840 \, d}"," ",0,"-1/840*(sqrt(2)*(525*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 175*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 525*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) + 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 - 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) - 30*sin(7/2*d*x + 7/2*c) + 21*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 525*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A/sqrt(a) - 140*(3*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 3*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*sqrt(2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/sqrt(a))/d","B",0
1155,1,553,0,0.703537," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{2} {\left(60 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 60 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 60 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{30 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{\sqrt{a}}}{60 \, d}"," ",0,"1/60*(sqrt(2)*(60*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 60*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 6*sin(5/2*d*x + 5/2*c) - 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 60*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A/sqrt(a) - 30*(sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/sqrt(a))/d","B",0
1156,1,373,0,0.659064," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} - \frac{3 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} C}{\sqrt{a}}}{6 \, d}"," ",0,"-1/6*((3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A/sqrt(a) - 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*C/sqrt(a))/d","B",0
1157,1,712,0,0.716736," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{\sqrt{a}} + \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} C}{\sqrt{a}}}{2 \, d}"," ",0,"-1/2*((sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*A/sqrt(a) + (sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*C/sqrt(a))/d","B",0
1158,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1159,1,2304,0,0.833818," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} A}{\sqrt{a}} - \frac{{\left(4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{16 \, d}"," ",0,"-1/16*(8*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*A/sqrt(a) - (4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
1160,1,3766,0,0.921103," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} + \frac{{\left(84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)) + (84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
1161,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1162,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1163,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1164,1,3153,0,0.903633," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 12 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(d x + c\right) + 4 \, {\left(3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(d x + c\right) - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(d x + c\right) + 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 4 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{{\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(d x + c\right)^{2} + \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 4 \, \sqrt{2} a \sin\left(d x + c\right)^{2} + 4 \, \sqrt{2} a \cos\left(d x + c\right) + 2 \, {\left(2 \, \sqrt{2} a \cos\left(d x + c\right) + \sqrt{2} a\right)} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sqrt{a}} + \frac{{\left(4 \, {\left(\sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 5 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 5 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*((3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 + 2*(6*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 2*sin(3/2*d*x + 3/2*c) + 2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 4*(3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 4*(3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + cos(3/2*d*x + 3/2*c) - cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*(2*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 8*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 8*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 4*sin(1/2*d*x + 1/2*c))*A/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 4*sqrt(2)*a*sin(d*x + c)^2 + 4*sqrt(2)*a*cos(d*x + c) + 2*(2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*sqrt(a)) + (4*(sin(2*d*x + 2*c) + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 5*(cos(2*d*x + 2*c)^2 + 4*(cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(2*d*x + 2*c)^2 + 4*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 5*(cos(2*d*x + 2*c)^2 + 4*(cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(2*d*x + 2*c)^2 + 4*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 4*(cos(2*d*x + 2*c) + 2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 4*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*sqrt(a)))/d","B",0
1165,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1166,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1167,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1169,-1,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1170,1,5530,0,1.327495," ","integrate((A+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\frac{{\left(19 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(3 \, d x + 3 \, c\right)^{2} + 684 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right)^{2} + 19 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(3 \, d x + 3 \, c\right)^{2} + 684 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 114 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 26 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 10 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 10 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 104 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 8 \, {\left(114 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 10 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 10 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 40 \, {\left(3 \, \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 12 \, {\left(76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(d x + c\right) + 4 \, {\left(38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(3 \, d x + 3 \, c\right) + 57 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right) + 38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + 13 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 13 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 52 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 16 \, {\left(57 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right) + 38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 13 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) - 20 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 24 \, {\left(38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) - 5 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 13 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) + 20 \, {\left(4 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 80 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(d x + c\right) - 208 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 52 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{{\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(d x + c\right)^{2} + \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 48 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 16 \, \sqrt{2} a^{2} \sin\left(d x + c\right)^{2} + 8 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2} + 2 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + 12 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 16 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(d x + c\right)\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sqrt{a}} - \frac{{\left(12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(11 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(11 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 48 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 48 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a}}}{32 \, d}"," ",0,"1/32*((19*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(4*d*x + 4*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 684*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 19*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(4*d*x + 4*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 684*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 + 2*(76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c) + 114*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 26*sin(7/2*d*x + 7/2*c) - 10*sin(5/2*d*x + 5/2*c) + 10*sin(3/2*d*x + 3/2*c) + 26*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c) + 104*(2*sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 2*sin(d*x + c))*cos(7/2*d*x + 7/2*c) + 8*(114*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sin(5/2*d*x + 5/2*c) + 10*sin(3/2*d*x + 3/2*c) + 26*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 40*(3*sin(2*d*x + 2*c) + 2*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 12*(76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sin(3/2*d*x + 3/2*c) + 26*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 8*(19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 26*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 4*(38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c) + 57*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 13*cos(7/2*d*x + 7/2*c) + 5*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c) - 13*cos(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) - 52*(4*cos(3*d*x + 3*c) + 6*cos(2*d*x + 2*c) + 4*cos(d*x + c) + 1)*sin(7/2*d*x + 7/2*c) + 16*(57*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 5*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c) - 13*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(6*cos(2*d*x + 2*c) + 4*cos(d*x + c) + 1)*sin(5/2*d*x + 5/2*c) + 24*(38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 5*cos(3/2*d*x + 3/2*c) - 13*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 20*(4*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - 80*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 208*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 52*sin(1/2*d*x + 1/2*c))*A/((sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*a^2*cos(3*d*x + 3*c)^2 + 36*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(d*x + c)^2 + sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 16*sqrt(2)*a^2*sin(3*d*x + 3*c)^2 + 36*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 48*sqrt(2)*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 16*sqrt(2)*a^2*sin(d*x + c)^2 + 8*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2 + 2*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2)*cos(4*d*x + 4*c) + 8*(6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2)*cos(3*d*x + 3*c) + 12*(4*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2)*cos(2*d*x + 2*c) + 4*(2*sqrt(2)*a^2*sin(3*d*x + 3*c) + 3*sqrt(2)*a^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(d*x + c))*sin(4*d*x + 4*c) + 16*(3*sqrt(2)*a^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(d*x + c))*sin(3*d*x + 3*c))*sqrt(a)) - (12*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(11*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(11*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 48*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 48*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2 + 2*(6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(4*d*x + 4*c) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c) + 4*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)))/d","B",0
1171,1,7863,0,1.328634," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 40 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 24 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 24 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, {\left(16 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 48 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 5 \, {\left(16 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 48 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 48 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(3 \, d x + 3 \, c\right) + 80 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(3 \, d x + 3 \, c\right) + 48 \, \cos\left(3 \, d x + 3 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 20 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 20 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} A}{{\left(16 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + \sqrt{2} a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 36 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 48 \, {\left(\sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a}} + \frac{{\left(44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(19 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(19 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 176 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 176 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a}}}{32 \, d}"," ",0,"1/32*((4*(3*sin(3/2*d*x + 3/2*c) + 5*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 40*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 24*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 24*(3*sin(3/2*d*x + 3/2*c) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*(3*sin(3/2*d*x + 3/2*c) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*(16*cos(3*d*x + 3*c)^2 + 2*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(4*cos(3*d*x + 3*c) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(4*cos(3*d*x + 3*c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sin(3*d*x + 3*c)^2 + 4*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 48*(sin(3*d*x + 3*c) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*cos(3*d*x + 3*c) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 5*(16*cos(3*d*x + 3*c)^2 + 2*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(4*cos(3*d*x + 3*c) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(4*cos(3*d*x + 3*c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sin(3*d*x + 3*c)^2 + 4*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 48*(sin(3*d*x + 3*c) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*cos(3*d*x + 3*c) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 48*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 80*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + 48*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*(3*cos(3/2*d*x + 3/2*c) + 5*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*(3*cos(3/2*d*x + 3/2*c) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*(3*cos(3/2*d*x + 3/2*c) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(4*cos(3*d*x + 3*c) + 1)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*sin(3/2*d*x + 3/2*c))*A/((16*sqrt(2)*a^2*cos(3*d*x + 3*c)^2 + sqrt(2)*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 36*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sqrt(2)*a^2*sin(3*d*x + 3*c)^2 + sqrt(2)*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 36*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sqrt(2)*a^2*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*sqrt(2)*a^2*cos(3*d*x + 3*c) + sqrt(2)*a^2 + 2*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 6*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 4*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + sqrt(2)*a^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(2*sqrt(2)*a^2*sin(3*d*x + 3*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 48*(sqrt(2)*a^2*sin(3*d*x + 3*c) + sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)) + (44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(19*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(19*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 176*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 176*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2 + 2*(6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(4*d*x + 4*c) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c) + 4*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)))/d","B",0
1172,-2,0,0,0.000000," ","integrate((A+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1173,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(9/2), x)","F",0
1174,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(7/2), x)","F",0
1175,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(5/2), x)","F",0
1176,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*cos(d*x + c)^(3/2), x)","F",0
1177,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
1178,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
1179,0,0,0,0.000000," ","integrate((B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
1180,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2), x)","F",0
1181,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2), x)","F",0
1182,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2), x)","F",0
1183,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
1184,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
1185,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
1186,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
1187,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1188,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1189,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1190,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1191,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1192,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1193,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1194,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1195,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1196,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1197,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1198,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1199,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1200,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1201,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1202,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1203,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1204,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1205,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1206,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1207,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1208,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1209,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1210,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1211,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1212,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1213,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1214,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1215,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1216,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1217,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
1218,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
1219,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
1220,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
1221,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1222,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1223,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1224,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1225,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1226,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
1227,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
1228,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1229,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1232,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
1234,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
1235,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1237,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1238,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1243,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1244,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1245,1,668,0,0.777035," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(1890 \, \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 420 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 252 \, \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 1890 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 420 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 252 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 45 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 252 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 420 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1890 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 18 \, \sqrt{2} {\left(7 \, {\left(15 \, \sin\left(3 \, d x + 3 \, c\right) + 5 \, \sin\left(2 \, d x + 2 \, c\right) + \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - {\left(105 \, \cos\left(3 \, d x + 3 \, c\right) + 35 \, \cos\left(2 \, d x + 2 \, c\right) + 7 \, \cos\left(d x + c\right) + 10\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 7 \, \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 35 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 105 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a} - 84 \, \sqrt{2} {\left(5 \, {\left(6 \, \sin\left(2 \, d x + 2 \, c\right) + \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - {\left(30 \, \cos\left(2 \, d x + 2 \, c\right) + 5 \, \cos\left(d x + c\right) + 6\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 5 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 30 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(1890*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 420*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 252*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 45*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 1890*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 420*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 252*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 45*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*sin(9/2*d*x + 9/2*c) + 45*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 252*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 420*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1890*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) - 18*sqrt(2)*(7*(15*sin(3*d*x + 3*c) + 5*sin(2*d*x + 2*c) + sin(d*x + c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - (105*cos(3*d*x + 3*c) + 35*cos(2*d*x + 2*c) + 7*cos(d*x + c) + 10)*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 7*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 35*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 105*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a) - 84*sqrt(2)*(5*(6*sin(2*d*x + 2*c) + sin(d*x + c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - (30*cos(2*d*x + 2*c) + 5*cos(d*x + c) + 6)*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 5*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 30*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a))/d","B",0
1246,1,508,0,0.798010," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(105 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 35 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 105 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 35 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 7 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 10 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 14 \, \sqrt{2} {\left(5 \, {\left(6 \, \sin\left(2 \, d x + 2 \, c\right) + \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - {\left(30 \, \cos\left(2 \, d x + 2 \, c\right) + 5 \, \cos\left(d x + c\right) + 6\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 5 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 30 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a} - 140 \, {\left(3 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(d x + c\right) - {\left(3 \, \sqrt{2} \cos\left(d x + c\right) + 2 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(3*sqrt(2)*(105*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 35*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 7*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 105*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 35*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 7*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 10*sin(7/2*d*x + 7/2*c) + 7*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) - 14*sqrt(2)*(5*(6*sin(2*d*x + 2*c) + sin(d*x + c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - (30*cos(2*d*x + 2*c) + 5*cos(d*x + c) + 6)*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 5*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 30*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a) - 140*(3*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(d*x + c) - (3*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a))/d","B",0
1247,1,321,0,0.764004," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 120 \, \sqrt{2} C \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 10 \, {\left(3 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(d x + c\right) - {\left(3 \, \sqrt{2} \cos\left(d x + c\right) + 2 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{60 \, d}"," ",0,"1/60*(sqrt(2)*(30*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 30*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 6*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 120*sqrt(2)*C*sqrt(a)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 10*(3*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(d*x + c) - (3*sqrt(2)*cos(d*x + c) + 2*sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a))/d","B",0
1248,1,380,0,0.752172," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 12 \, \sqrt{2} B \sqrt{a} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 3 \, C \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)}}{6 \, d}"," ",0,"1/6*(sqrt(2)*(3*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) + 12*sqrt(2)*B*sqrt(a)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 3*C*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)))/d","B",0
1249,1,970,0,0.764039," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, B \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) + 2*B*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)) - (4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
1250,1,2167,0,0.911485," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, A \sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} - \frac{4 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{16 \, d}"," ",0,"1/16*(8*A*sqrt(a)*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2)) - 4*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
1251,1,4002,0,1.057053," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{6 \, {\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 6*(12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + (60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
1252,1,6492,0,1.316490," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 12 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 12 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{8 \, {\left(60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 60 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 168 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 60 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{{\left(420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 420 \, {\left(\sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 105 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 500 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1596 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 140 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 420 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 12*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 3*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 12*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + 8*(60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 60*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 168*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 20*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 60*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*B*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + (420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(15/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(13/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(11/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(9/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c))) - 420*(sqrt(2)*sin(8*d*x + 8*c) + 4*sqrt(2)*sin(6*d*x + 6*c) + 6*sqrt(2)*sin(4*d*x + 4*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 105*(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(15/2*arctan2(sin(d*x + c), cos(d*x + c))) - 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(13/2*arctan2(sin(d*x + c), cos(d*x + c))) - 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/2*arctan2(sin(d*x + c), cos(d*x + c))) - 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/2*arctan2(sin(d*x + c), cos(d*x + c))) + 500*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1596*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*arctan2(sin(d*x + c), cos(d*x + c))) + 140*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 420*(sqrt(2)*cos(8*d*x + 8*c) + 4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
1253,1,862,0,0.824129," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{21 \, \sqrt{2} {\left(3630 \, a \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 990 \, a \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 429 \, a \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 165 \, a \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 3630 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 990 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 429 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 165 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 55 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, a \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 165 \, a \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 429 \, a \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 990 \, a \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3630 \, a \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 44 \, \sqrt{2} {\left(189 \, {\left(10 \, a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 7 \, {\left(270 \, a \cos\left(4 \, d x + 4 \, c\right) + 27 \, a \cos\left(2 \, d x + 2 \, c\right) + 5 \, a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 135 \, a \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 189 \, a \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1050 \, a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1890 \, a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} - 132 \, \sqrt{2} {\left(175 \, a \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 5 \, {\left(35 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 126 \, a \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 175 \, a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1470 \, a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{110880 \, d}"," ",0,"1/110880*(21*sqrt(2)*(3630*a*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 990*a*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 429*a*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 165*a*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 55*a*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 3630*a*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 990*a*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 429*a*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 165*a*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 55*a*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 30*a*sin(11/2*d*x + 11/2*c) + 55*a*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 165*a*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 429*a*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 990*a*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3630*a*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) - 44*sqrt(2)*(189*(10*a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 7*(270*a*cos(4*d*x + 4*c) + 27*a*cos(2*d*x + 2*c) + 5*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 135*a*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 189*a*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1050*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1890*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) - 132*sqrt(2)*(175*a*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 5*(35*a*cos(2*d*x + 2*c) + 6*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 126*a*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 175*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1470*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1254,1,703,0,0.789353," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3780 \, a \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1050 \, a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 378 \, a \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 3780 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 1050 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 378 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 135 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 378 \, a \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1050 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 3780 \, a \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 6 \, \sqrt{2} {\left(175 \, a \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 5 \, {\left(35 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 126 \, a \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 175 \, a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1470 \, a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} - 504 \, {\left(10 \, \sqrt{2} a \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 10 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(10 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(3780*a*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 1050*a*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 378*a*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 135*a*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 3780*a*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 1050*a*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 378*a*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 135*a*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a*sin(9/2*d*x + 9/2*c) + 135*a*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 378*a*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1050*a*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 3780*a*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) - 6*sqrt(2)*(175*a*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 5*(35*a*cos(2*d*x + 2*c) + 6*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 126*a*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 175*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1470*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) - 504*(10*sqrt(2)*a*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 5*sqrt(2)*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 10*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (10*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1255,1,513,0,0.775006," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 84 \, {\left(10 \, \sqrt{2} a \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 10 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(10 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} + 280 \, {\left(\sqrt{2} a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(sqrt(2)*(735*a*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 175*a*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 63*a*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 735*a*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*a*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 63*a*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 30*a*sin(7/2*d*x + 7/2*c) + 63*a*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*a*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 735*a*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) - 84*(10*sqrt(2)*a*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 5*sqrt(2)*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 10*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (10*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) + 280*(sqrt(2)*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 9*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1256,1,757,0,0.805733," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 20 \, {\left(\sqrt{2} a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} + 30 \, {\left(4 \, \sqrt{2} a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} C \sqrt{a}}{60 \, d}"," ",0,"1/60*(3*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A*sqrt(a) + 20*(sqrt(2)*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 9*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) + 30*(4*sqrt(2)*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*C*sqrt(a))/d","B",0
1257,1,1895,0,0.819337," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{20 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 6 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 40 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 20 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, a \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 5 \, a \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 5 \, a \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 5 \, a \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} B \sqrt{a} - \frac{15 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 2 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 6 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{60 \, d}"," ",0,"1/60*(20*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 6*(2*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 40*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 2*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*a*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 5*a*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 5*a*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 5*a*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*B*sqrt(a) - 15*(2*sqrt(2)*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 6*sqrt(2)*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 5*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 2*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/2*d*x + 7/2*c) - 6*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/2*d*x + 5/2*c) + 2*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
1258,1,3661,0,0.936419," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(\sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 8 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + \frac{4 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} B \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1}}{16 \, d}"," ",0,"1/16*(4*sqrt(2)*(sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 8*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 4*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*B*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1))/d","B",0
1259,1,5748,0,1.128594," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\left(a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 2 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 4 \, {\left(\sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{6 \, {\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1} - \frac{{\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"1/96*(24*(3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + 3*(a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 2*(2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 2*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 4*(sqrt(2)*a*cos(3/2*d*x + 3/2*c) - sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - 6*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*B*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1))/d","B",0
1260,1,8121,0,1.444612," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(56 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 28 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 4 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(3 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 7 \, {\left(a \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, a \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, {\left(2 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, \sqrt{2} a \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 28 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 7 \, \sqrt{2} a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1} + \frac{8 \, {\left(132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 132 \, {\left(\sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 33 \, {\left(a \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 216 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 132 \, {\left(\sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{3 \, {\left(300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 300 \, {\left(\sqrt{2} a \sin\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 75 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{15}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{13}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 228 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1140 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 300 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right) + 4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{768 \, d}"," ",0,"-1/768*(48*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(2*(2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 8*(132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 132*(sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 3*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 33*(a*cos(6*d*x + 6*c)^2 + 9*a*cos(4*d*x + 4*c)^2 + 9*a*cos(2*d*x + 2*c)^2 + a*sin(6*d*x + 6*c)^2 + 9*a*sin(4*d*x + 4*c)^2 + 18*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a*sin(2*d*x + 2*c)^2 + 2*(3*a*cos(4*d*x + 4*c) + 3*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 6*(3*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 6*a*cos(2*d*x + 2*c) + 6*(a*sin(4*d*x + 4*c) + a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 216*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 132*(sqrt(2)*a*cos(6*d*x + 6*c) + 3*sqrt(2)*a*cos(4*d*x + 4*c) + 3*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + 3*(300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 300*(sqrt(2)*a*sin(8*d*x + 8*c) + 4*sqrt(2)*a*sin(6*d*x + 6*c) + 6*sqrt(2)*a*sin(4*d*x + 4*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 75*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(15/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(13/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 228*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1140*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 300*(sqrt(2)*a*cos(8*d*x + 8*c) + 4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a)/(2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1))/d","B",0
1261,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1262,1,1135,0,0.859577," ","integrate(cos(d*x+c)^(13/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3783780 \, a^{2} \cos\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 1066065 \, a^{2} \cos\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 459459 \, a^{2} \cos\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 193050 \, a^{2} \cos\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 70070 \, a^{2} \cos\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \cos\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 3783780 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{12}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 1066065 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{10}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 459459 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{8}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 193050 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{6}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 70070 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{4}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 20475 \, a^{2} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) \sin\left(\frac{2}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 6930 \, a^{2} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, a^{2} \sin\left(\frac{11}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 70070 \, a^{2} \sin\left(\frac{9}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 193050 \, a^{2} \sin\left(\frac{7}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 459459 \, a^{2} \sin\left(\frac{5}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 1066065 \, a^{2} \sin\left(\frac{3}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 3783780 \, a^{2} \sin\left(\frac{1}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 1144 \, \sqrt{2} {\left(225 \, a^{2} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 378 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4095 \, a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 63 \, {\left(65 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7 \, {\left(585 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 54 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 5 \, a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a} + 130 \, {\left(770 \, \sqrt{2} a^{2} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1287 \, \sqrt{2} a^{2} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 6930 \, \sqrt{2} a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8778 \, \sqrt{2} a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 63756 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 33 \, {\left(266 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 39 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, {\left(2926 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 429 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 42 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a}}{2882880 \, d}"," ",0,"1/2882880*(sqrt(2)*(3783780*a^2*cos(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 1066065*a^2*cos(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 459459*a^2*cos(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 193050*a^2*cos(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 70070*a^2*cos(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) + 20475*a^2*cos(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c)))*sin(13/2*d*x + 13/2*c) - 3783780*a^2*cos(13/2*d*x + 13/2*c)*sin(12/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 1066065*a^2*cos(13/2*d*x + 13/2*c)*sin(10/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 459459*a^2*cos(13/2*d*x + 13/2*c)*sin(8/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 193050*a^2*cos(13/2*d*x + 13/2*c)*sin(6/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 70070*a^2*cos(13/2*d*x + 13/2*c)*sin(4/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 20475*a^2*cos(13/2*d*x + 13/2*c)*sin(2/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 6930*a^2*sin(13/2*d*x + 13/2*c) + 20475*a^2*sin(11/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 70070*a^2*sin(9/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 193050*a^2*sin(7/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 459459*a^2*sin(5/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 1066065*a^2*sin(3/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 3783780*a^2*sin(1/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))))*A*sqrt(a) + 1144*sqrt(2)*(225*a^2*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 378*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2100*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4095*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 63*(65*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7*(585*a^2*cos(4*d*x + 4*c) + 54*a^2*cos(2*d*x + 2*c) + 5*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a) + 130*(770*sqrt(2)*a^2*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1287*sqrt(2)*a^2*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6930*sqrt(2)*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8778*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 63756*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 33*(266*sqrt(2)*a^2*sin(4*d*x + 4*c) + 39*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*(2926*sqrt(2)*a^2*cos(4*d*x + 4*c) + 429*sqrt(2)*a^2*cos(2*d*x + 2*c) + 42*sqrt(2)*a^2)*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a))/d","B",0
1263,1,925,0,0.813213," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{5 \, \sqrt{2} {\left(31878 \, a^{2} \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 8778 \, a^{2} \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 3465 \, a^{2} \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1287 \, a^{2} \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 31878 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 8778 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 3465 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1287 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 385 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 126 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1287 \, a^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3465 \, a^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 8778 \, a^{2} \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 31878 \, a^{2} \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + 44 \, \sqrt{2} {\left(225 \, a^{2} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 378 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4095 \, a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 63 \, {\left(65 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7 \, {\left(585 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 54 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 5 \, a^{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} - 660 \, \sqrt{2} {\left(77 \, a^{2} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 42 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 77 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 630 \, a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(77 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 6 \, a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{110880 \, d}"," ",0,"1/110880*(5*sqrt(2)*(31878*a^2*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 8778*a^2*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 3465*a^2*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 1287*a^2*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 385*a^2*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 31878*a^2*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 8778*a^2*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 3465*a^2*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1287*a^2*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 385*a^2*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 126*a^2*sin(11/2*d*x + 11/2*c) + 385*a^2*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1287*a^2*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3465*a^2*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 8778*a^2*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 31878*a^2*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*A*sqrt(a) + 44*sqrt(2)*(225*a^2*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 378*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2100*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4095*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 63*(65*a^2*sin(4*d*x + 4*c) + 6*a^2*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7*(585*a^2*cos(4*d*x + 4*c) + 54*a^2*cos(2*d*x + 2*c) + 5*a^2)*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) - 660*sqrt(2)*(77*a^2*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 42*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 77*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 630*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (77*a^2*cos(2*d*x + 2*c) + 6*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1264,1,751,0,0.791000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 30 \, \sqrt{2} {\left(77 \, a^{2} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 42 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 77 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 630 \, a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(77 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 6 \, a^{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} - 168 \, {\left(75 \, \sqrt{2} a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C \sqrt{a}}{5040 \, d}"," ",0,"1/5040*(sqrt(2)*(8190*a^2*cos(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 2100*a^2*cos(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 756*a^2*cos(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) + 225*a^2*cos(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c)))*sin(9/2*d*x + 9/2*c) - 8190*a^2*cos(9/2*d*x + 9/2*c)*sin(8/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 2100*a^2*cos(9/2*d*x + 9/2*c)*sin(2/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 756*a^2*cos(9/2*d*x + 9/2*c)*sin(4/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 225*a^2*cos(9/2*d*x + 9/2*c)*sin(2/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 70*a^2*sin(9/2*d*x + 9/2*c) + 225*a^2*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 756*a^2*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 2100*a^2*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 8190*a^2*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))*A*sqrt(a) - 30*sqrt(2)*(77*a^2*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 42*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 77*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 630*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (77*a^2*cos(2*d*x + 2*c) + 6*a^2)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) - 168*(75*sqrt(2)*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 25*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(25*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C*sqrt(a))/d","B",0
1265,1,1005,0,0.814173," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{5 \, \sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A \sqrt{a} - 28 \, {\left(75 \, \sqrt{2} a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 75 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a} + 140 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 30 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} C \sqrt{a}}{840 \, d}"," ",0,"1/840*(5*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A*sqrt(a) - 28*(75*sqrt(2)*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 25*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(25*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a) + 140*(2*sqrt(2)*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 30*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*C*sqrt(a))/d","B",0
1266,1,8464,0,1.180094," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{42 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 210 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} B \sqrt{a} - \frac{5 \, {\left(1449 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} \sin\left(2 \, d x + 2 \, c\right) - 1260 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1449 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(25 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 198 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 69 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 98 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, {\left(50 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 50 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(50 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 21 \, {\left(60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 7 \, {\left(9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} + 138 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 50 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 105 \, {\left(12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 252 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 63 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1260 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{1260 \, d}"," ",0,"1/1260*(42*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 210*(2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 3*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*B*sqrt(a) - 5*(1449*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^3*sin(2*d*x + 2*c) - 1260*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 1449*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^3 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 5*(5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (25*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 198*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*cos(2*d*x + 2*c)^2 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 69*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + (25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 5*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c)^2 - 35*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 135*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) - 98*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 390*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(7/2*d*x + 7/2*c) + 21*(50*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) + 50*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 120*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 10*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (50*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 69*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c) - 21*(60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) + 12*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 35*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(13/2*d*x + 13/2*c) + 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(11/2*d*x + 11/2*c) + 7*(9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 4*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(9/2*d*x + 9/2*c) - 390*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/2*d*x + 7/2*c) - 21*(69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 69*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*cos(2*d*x + 2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*sin(2*d*x + 2*c)^2 + 12*sqrt(2)*a^2 + 138*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - sqrt(2)*a^2*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 - 50*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 24*sqrt(2)*a^2)*cos(2*d*x + 2*c) - 10*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c) + 105*(12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c) - 252*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c) - 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 63*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1260*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + cos(1/2*d*x + 1/2*c)^2 + 2*(cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c) + sin(1/2*d*x + 1/2*c)^2))/d","B",0
1267,1,5414,0,4.221893," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} {\left(30 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 30 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 4 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a} + \frac{12 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{3} - 4 \, \sqrt{2} a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 5 \, {\left(a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 5 \, {\left(a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 5 \, {\left(a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 5 \, {\left(a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, a^{2} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{a}}{\cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}} - \frac{3 \, {\left(88 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 56 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 28 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 44 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 76 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(22 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 14 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 38 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(14 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 22 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 19 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(11 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19 \, {\left(a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 44 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 28 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} C \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{48 \, d}"," ",0,"1/48*(4*sqrt(2)*(30*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 30*a^2*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*a^2*sin(3/2*d*x + 3/2*c) + 30*a^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a) + 12*(4*sqrt(2)*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^3 - 4*sqrt(2)*a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(2*sqrt(2)*a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 5*(a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 5*(a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 5*(a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 5*(a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*a^2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 4*(2*sqrt(2)*a^2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*a^2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(a)/(cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2) - 3*(88*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 56*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 28*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 44*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(4*d*x + 4*c)^2 - 76*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 2*(22*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) - 14*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 38*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c))*cos(4*d*x + 4*c) - 4*(14*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 22*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) + 4*(11*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c) - 7*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c) + 7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c) - 19*(a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 44*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) + 28*(2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c) + 8*(7*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) - 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*C*sqrt(a)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
1268,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1269,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1270,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1271,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,1,970,0,0.861622," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{2} {\left(525 \, \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 175 \, \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 525 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) + 420 \, \log\left(\cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 1\right) - 30 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 525 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} + \frac{28 \, {\left(30 \, \sqrt{2} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, {\left(10 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 15 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 15 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 30 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B}{\sqrt{a}} - \frac{140 \, {\left(3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{\sqrt{a}}}{840 \, d}"," ",0,"-1/840*(sqrt(2)*(525*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 175*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 525*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 175*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) + 420*log(cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 + sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))^2 - 2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 1) - 30*sin(7/2*d*x + 7/2*c) + 21*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 175*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 525*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*A/sqrt(a) + 28*(30*sqrt(2)*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*(10*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 15*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 15*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 5*sqrt(2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 30*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/sqrt(a) - 140*(3*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 3*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*sqrt(2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/sqrt(a))/d","B",0
1273,1,774,0,0.816481," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{\sqrt{2} {\left(60 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 60 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 30 \, \log\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 1\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 60 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} + \frac{10 \, {\left(3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 6 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B}{\sqrt{a}} - \frac{30 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{\sqrt{a}}}{60 \, d}"," ",0,"1/60*(sqrt(2)*(60*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 5*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 60*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 5*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 30*log(cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 + sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))^2 - 2*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 1) + 6*sin(5/2*d*x + 5/2*c) - 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 60*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*A/sqrt(a) + 10*(3*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 3*sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*sqrt(2)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 6*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/sqrt(a) - 30*(sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/sqrt(a))/d","B",0
1274,1,566,0,0.750168," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A}{\sqrt{a}} + \frac{3 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B}{\sqrt{a}} - \frac{3 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} C}{\sqrt{a}}}{6 \, d}"," ",0,"-1/6*((3*sqrt(2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3/2*d*x + 3/2*c) - 3*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A/sqrt(a) + 3*(sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - sqrt(2)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/sqrt(a) - 3*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*C/sqrt(a))/d","B",0
1275,1,800,0,0.779823," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{\sqrt{a}} - \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} B}{\sqrt{a}} + \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} C}{\sqrt{a}}}{2 \, d}"," ",0,"-1/2*((sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*A/sqrt(a) - (sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*B/sqrt(a) + (sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*C/sqrt(a))/d","B",0
1276,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1277,1,3334,0,1.010727," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right)\right)} A}{\sqrt{a}} + \frac{4 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} - \frac{{\left(4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{16 \, d}"," ",0,"-1/16*(8*(sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2))*A/sqrt(a) + 4*(4*sqrt(2)*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)) - (4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
1278,1,5590,0,1.140255," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} - \frac{6 \, {\left(4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 7 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 20 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}} + \frac{{\left(84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 312 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 84 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 27 \, {\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 48 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 312 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 100 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 84 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a}}}{96 \, d}"," ",0,"-1/96*(24*(4*sqrt(2)*cos(3/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))*sin(2*d*x + 2*c) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 1) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/2*arctan2(sin(d*x + c), cos(d*x + c))) + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))))*A/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a)) - 6*(4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 7*(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 8*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 4*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 20*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(a)) + (84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 312*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 84*(sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 3*sqrt(2)*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 27*(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 48*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 312*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 100*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 84*(sqrt(2)*cos(6*d*x + 6*c) + 3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*sqrt(a)))/d","B",0
1279,1,890,0,0.885343," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} - {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} B \sqrt{a} - \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} A b}{\sqrt{a}} + \frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} B b}{\sqrt{a}}}{2 \, d}"," ",0,"-1/2*((sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) - (sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*B*sqrt(a) - (sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*A*b/sqrt(a) + (sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - sqrt(2)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*B*b/sqrt(a))/d","B",0
1280,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1281,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1282,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1283,1,4285,0,0.915070," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 12 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(d x + c\right) + 4 \, {\left(3 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(d x + c\right) - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(d x + c\right) + 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 4 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{{\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(d x + c\right)^{2} + \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 4 \, \sqrt{2} a \sin\left(d x + c\right)^{2} + 4 \, \sqrt{2} a \cos\left(d x + c\right) + 2 \, {\left(2 \, \sqrt{2} a \cos\left(d x + c\right) + \sqrt{2} a\right)} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sqrt{a}} + \frac{{\left(4 \, {\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + {\left(2 \, {\left(2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, {\left(\cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} B}{{\left(\sqrt{2} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sqrt{2} a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sqrt{2} a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sqrt{2} a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sqrt{2} a \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 4 \, \sqrt{2} a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a\right)} \sqrt{a}} + \frac{{\left(4 \, {\left(\sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 2 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 5 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 5 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 8 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*((3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 12*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 + 2*(6*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 2*sin(3/2*d*x + 3/2*c) + 2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 4*(3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 2*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 4*(3*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + cos(3/2*d*x + 3/2*c) - cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*(2*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) + 8*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 8*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 3*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 4*sin(1/2*d*x + 1/2*c))*A/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(d*x + c)^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(d*x + c) + 4*sqrt(2)*a*sin(d*x + c)^2 + 4*sqrt(2)*a*cos(d*x + c) + 2*(2*sqrt(2)*a*cos(d*x + c) + sqrt(2)*a)*cos(2*d*x + 2*c) + sqrt(2)*a)*sqrt(a)) + (4*(sin(3/2*d*x + 3/2*c) - sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(sin(3/2*d*x + 3/2*c) - sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + (2*(2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (2*(2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 4*(cos(3/2*d*x + 3/2*c) - cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(cos(3/2*d*x + 3/2*c) - cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sin(3/2*d*x + 3/2*c) - 4*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*B/((sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sqrt(2)*a*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sqrt(2)*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sqrt(2)*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sqrt(2)*a*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*sqrt(2)*a*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(2*sqrt(2)*a*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sqrt(a)) + (4*(sin(2*d*x + 2*c) + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 2*(sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 5*(cos(2*d*x + 2*c)^2 + 4*(cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(2*d*x + 2*c)^2 + 4*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 5*(cos(2*d*x + 2*c)^2 + 4*(cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(2*d*x + 2*c)^2 + 4*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 4*(cos(2*d*x + 2*c) + 2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 4*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*sqrt(a)))/d","B",0
1284,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1285,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1286,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1287,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1288,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1289,1,8402,0,1.690081," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{{\left(19 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(3 \, d x + 3 \, c\right)^{2} + 684 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right)^{2} + 19 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(3 \, d x + 3 \, c\right)^{2} + 684 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 304 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 114 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 26 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 10 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 10 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 104 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 8 \, {\left(114 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 10 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 10 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 40 \, {\left(3 \, \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 12 \, {\left(76 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \cos\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 26 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(d x + c\right) + 4 \, {\left(38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(3 \, d x + 3 \, c\right) + 57 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right) + 38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + 13 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 13 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 52 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 16 \, {\left(57 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(2 \, d x + 2 \, c\right) + 38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) + 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 13 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) - 20 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 24 \, {\left(38 \, {\left(\log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)\right)} \sin\left(d x + c\right) - 5 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 13 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) + 20 \, {\left(4 \, \cos\left(d x + c\right) + 1\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 80 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(d x + c\right) - 208 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(d x + c\right) + 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 19 \, \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 52 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A}{{\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(d x + c\right)^{2} + \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 48 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + 16 \, \sqrt{2} a^{2} \sin\left(d x + c\right)^{2} + 8 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2} + 2 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + 12 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(d x + c\right) + \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 16 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(d x + c\right)\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sqrt{a}} + \frac{{\left(4 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 40 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 24 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 24 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, {\left(3 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, {\left(16 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 48 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 5 \, {\left(16 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 48 \, {\left(\sin\left(3 \, d x + 3 \, c\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 36 \, \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 48 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(3 \, d x + 3 \, c\right) + 80 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(3 \, d x + 3 \, c\right) + 48 \, \cos\left(3 \, d x + 3 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 3 \, \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 20 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 12 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 24 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 \, {\left(3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 20 \, {\left(4 \, \cos\left(3 \, d x + 3 \, c\right) + 1\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} B}{{\left(16 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + \sqrt{2} a^{2} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 36 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 32 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 8 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 12 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 4 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{8}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 48 \, {\left(\sqrt{2} a^{2} \sin\left(3 \, d x + 3 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a}} - \frac{{\left(12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(11 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 12 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(11 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 3 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 48 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 48 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} C}{{\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a}}}{32 \, d}"," ",0,"1/32*((19*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(4*d*x + 4*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c)^2 + 684*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c)^2 + 19*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(4*d*x + 4*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c)^2 + 684*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c)^2 + 304*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c)^2 + 2*(76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(3*d*x + 3*c) + 114*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 26*sin(7/2*d*x + 7/2*c) - 10*sin(5/2*d*x + 5/2*c) + 10*sin(3/2*d*x + 3/2*c) + 26*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c) + 104*(2*sin(3*d*x + 3*c) + 3*sin(2*d*x + 2*c) + 2*sin(d*x + c))*cos(7/2*d*x + 7/2*c) + 8*(114*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(2*d*x + 2*c) + 76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) - 10*sin(5/2*d*x + 5/2*c) + 10*sin(3/2*d*x + 3/2*c) + 26*sin(1/2*d*x + 1/2*c))*cos(3*d*x + 3*c) + 40*(3*sin(2*d*x + 2*c) + 2*sin(d*x + c))*cos(5/2*d*x + 5/2*c) + 12*(76*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*cos(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 10*sin(3/2*d*x + 3/2*c) + 26*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 8*(19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 26*sin(1/2*d*x + 1/2*c))*cos(d*x + c) + 4*(38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(3*d*x + 3*c) + 57*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 13*cos(7/2*d*x + 7/2*c) + 5*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c) - 13*cos(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) - 52*(4*cos(3*d*x + 3*c) + 6*cos(2*d*x + 2*c) + 4*cos(d*x + c) + 1)*sin(7/2*d*x + 7/2*c) + 16*(57*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(2*d*x + 2*c) + 38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) + 5*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c) - 13*cos(1/2*d*x + 1/2*c))*sin(3*d*x + 3*c) - 20*(6*cos(2*d*x + 2*c) + 4*cos(d*x + c) + 1)*sin(5/2*d*x + 5/2*c) + 24*(38*(log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))*sin(d*x + c) - 5*cos(3/2*d*x + 3/2*c) - 13*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) + 20*(4*cos(d*x + c) + 1)*sin(3/2*d*x + 3/2*c) - 80*cos(3/2*d*x + 3/2*c)*sin(d*x + c) - 208*cos(1/2*d*x + 1/2*c)*sin(d*x + c) + 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - 19*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1) + 52*sin(1/2*d*x + 1/2*c))*A/((sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*a^2*cos(3*d*x + 3*c)^2 + 36*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(d*x + c)^2 + sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 16*sqrt(2)*a^2*sin(3*d*x + 3*c)^2 + 36*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 48*sqrt(2)*a^2*sin(2*d*x + 2*c)*sin(d*x + c) + 16*sqrt(2)*a^2*sin(d*x + c)^2 + 8*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2 + 2*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2)*cos(4*d*x + 4*c) + 8*(6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2)*cos(3*d*x + 3*c) + 12*(4*sqrt(2)*a^2*cos(d*x + c) + sqrt(2)*a^2)*cos(2*d*x + 2*c) + 4*(2*sqrt(2)*a^2*sin(3*d*x + 3*c) + 3*sqrt(2)*a^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(d*x + c))*sin(4*d*x + 4*c) + 16*(3*sqrt(2)*a^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(d*x + c))*sin(3*d*x + 3*c))*sqrt(a)) + (4*(3*sin(3/2*d*x + 3/2*c) + 5*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 40*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 24*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 24*(3*sin(3/2*d*x + 3/2*c) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*(3*sin(3/2*d*x + 3/2*c) - 5*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*(16*cos(3*d*x + 3*c)^2 + 2*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(4*cos(3*d*x + 3*c) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(4*cos(3*d*x + 3*c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sin(3*d*x + 3*c)^2 + 4*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 48*(sin(3*d*x + 3*c) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*cos(3*d*x + 3*c) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 5*(16*cos(3*d*x + 3*c)^2 + 2*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 12*(4*cos(3*d*x + 3*c) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*(4*cos(3*d*x + 3*c) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sin(3*d*x + 3*c)^2 + 4*(2*sin(3*d*x + 3*c) + 3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 48*(sin(3*d*x + 3*c) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 36*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*cos(3*d*x + 3*c) + 1)*log(cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 48*cos(3/2*d*x + 3/2*c)*sin(3*d*x + 3*c) + 80*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(3*d*x + 3*c) + 48*cos(3*d*x + 3*c)*sin(3/2*d*x + 3/2*c) - 4*(3*cos(3/2*d*x + 3/2*c) + 5*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 20*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*(4*cos(3*d*x + 3*c) + 6*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*(3*cos(3/2*d*x + 3/2*c) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*(3*cos(3/2*d*x + 3/2*c) - 5*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 20*(4*cos(3*d*x + 3*c) + 1)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*sin(3/2*d*x + 3/2*c))*B/((16*sqrt(2)*a^2*cos(3*d*x + 3*c)^2 + sqrt(2)*a^2*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 36*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 16*sqrt(2)*a^2*sin(3*d*x + 3*c)^2 + sqrt(2)*a^2*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 36*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 32*sqrt(2)*a^2*sin(3*d*x + 3*c)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 8*sqrt(2)*a^2*cos(3*d*x + 3*c) + sqrt(2)*a^2 + 2*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 6*sqrt(2)*a^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + 4*sqrt(2)*a^2*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a^2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(4*sqrt(2)*a^2*cos(3*d*x + 3*c) + sqrt(2)*a^2)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*(2*sqrt(2)*a^2*sin(3*d*x + 3*c) + 3*sqrt(2)*a^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 48*(sqrt(2)*a^2*sin(3*d*x + 3*c) + sqrt(2)*a^2*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)) - (12*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(11*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 12*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 12*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(11*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 48*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 48*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*C/((sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2 + 2*(6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(4*d*x + 4*c) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + 4*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 6*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c) + 4*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 6*sqrt(2)*a^2*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)))/d","B",0
1290,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1291,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1292,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1293,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1294,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1295,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1296,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1297,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1298,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1300,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1301,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1302,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1303,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1304,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1305,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1306,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1307,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1308,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1309,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1310,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1311,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1315,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1316,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
1319,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
1320,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
1321,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1322,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1323,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1324,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
1325,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
1326,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
1327,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1331,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1332,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1334,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
1335,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
1336,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
1337,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1338,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1339,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1340,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1341,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
1342,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
1343,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
1344,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
1345,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
1346,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
1347,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
1348,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1349,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
1350,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
1351,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
1352,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
1353,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
1354,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1355,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1356,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(7/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1357,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1358,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
1359,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1360,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1361,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1362,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*sec(d*x+c)+b*B*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \sec\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \sec\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*sec(d*x + c)^2 + A*a + (B*a + A*b)*sec(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
1363,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1364,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1365,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1366,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1367,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1368,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1369,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1370,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1371,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \sec\left(d x + c\right)^{2} + B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*sec(d*x + c)^2 + B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
1372,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1373,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
