1,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(5/2), x)","F",0
2,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(3/2), x)","F",0
3,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c)), x)","F",0
4,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c)), x)","F",0
5,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(3/2), x)","F",0
6,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(5/2), x)","F",0
7,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^2, x)","F",0
8,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c), x)","F",0
9,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3), x)","F",0
10,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c), x)","F",0
11,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*cos(d*x + c)^2, x)","F",0
12,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
13,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
14,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3), x)","F",0
15,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
16,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
17,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
18,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
19,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(2/3), x)","F",0
20,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(2/3), x)","F",0
21,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(2/3), x)","F",0
22,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^2/(b*sec(d*x + c))^(4/3), x)","F",0
23,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
24,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\left(b \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c))^(4/3), x)","F",0
25,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/(b*sec(d*x + c))^(4/3), x)","F",0
26,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^2/(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))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + 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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(4/3)*sec(d*x + c)^m, x)","F",0
28,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(2/3)*sec(d*x + c)^m, x)","F",0
29,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^(1/3)*sec(d*x + c)^m, x)","F",0
30,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(1/3), x)","F",0
31,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(2/3), x)","F",0
32,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^m/(b*sec(d*x + c))^(4/3), x)","F",0
33,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^m, x)","F",0
34,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^2, x)","F",0
35,0,0,0,0.000000," ","integrate(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c), x)","F",0
36,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \left(b \sec\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n, x)","F",0
37,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c), x)","F",0
38,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*cos(d*x + c)^2, x)","F",0
39,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sec(d*x + c)^(3/2), x)","F",0
40,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n*sqrt(sec(d*x + c)), x)","F",0
41,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sqrt(sec(d*x + c)), x)","F",0
42,0,0,0,0.000000," ","integrate((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c))^n/sec(d*x + c)^(3/2), x)","F",0
43,1,200,0,0.332590," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),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)} B a - 15 \, A 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 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)}}{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))*B*a - 15*A*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*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)))/d","A",0
44,1,163,0,0.336102," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a - 3 \, 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)} - 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 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a - 3*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)) - 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)))/d","A",0
45,1,127,0,0.334533," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a - 3 \, 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)} - 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)} + 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))*B*a - 3*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)) - 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)) + 12*A*a*tan(d*x + c))/d","A",0
46,1,88,0,0.322165," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} - 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 4 \, A a \tan\left(d x + c\right) - 4 \, B a \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(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)) - 4*A*a*log(sec(d*x + c) + tan(d*x + c)) - 4*A*a*tan(d*x + c) - 4*B*a*tan(d*x + c))/d","A",0
47,1,56,0,0.318688," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} A a + A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + B a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + B a \tan\left(d x + c\right)}{d}"," ",0,"((d*x + c)*A*a + A*a*log(sec(d*x + c) + tan(d*x + c)) + B*a*log(sec(d*x + c) + tan(d*x + c)) + B*a*tan(d*x + c))/d","A",0
48,1,58,0,0.326445," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),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)} + 2 \, A a \sin\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)) + 2*A*a*sin(d*x + c))/d","A",0
49,1,55,0,0.323925," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),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 \, 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*A*a*sin(d*x + c) + 4*B*a*sin(d*x + c))/d","A",0
50,1,79,0,0.322855," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),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 \, B 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*B*a*sin(d*x + c))/d","A",0
51,1,101,0,0.336074," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),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}{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)/d","A",0
52,1,124,0,0.341407," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),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}{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)/d","A",0
53,1,278,0,0.345997," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A 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)} B a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} - 15 \, 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)} - 30 \, 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)} - 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)}}{240 \, d}"," ",0,"1/240*(160*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 - 15*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)) - 30*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)) - 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)))/d","A",0
54,1,230,0,0.345797," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} - 3 \, 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)} - 24 \, 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 \, 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)} + 48 \, A a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 32*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 - 3*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)) - 24*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*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)) + 48*A*a^2*tan(d*x + c))/d","A",0
55,1,167,0,0.341263," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} - 3 \, 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)} - 6 \, 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 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 24 \, A a^{2} \tan\left(d x + c\right) + 12 \, B a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 - 3*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)) - 6*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*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 24*A*a^2*tan(d*x + c) + 12*B*a^2*tan(d*x + c))/d","A",0
56,1,128,0,0.326421," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{2} - 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)} + 8 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, B a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, A a^{2} \tan\left(d x + c\right) + 8 \, B a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a^2 - 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)) + 8*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 4*B*a^2*log(sec(d*x + c) + tan(d*x + c)) + 4*A*a^2*tan(d*x + c) + 8*B*a^2*tan(d*x + c))/d","A",0
57,1,105,0,0.338324," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{2} + 2 \, {\left(d x + c\right)} B a^{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 \, 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 \, A a^{2} \sin\left(d x + c\right) + 2 \, B a^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*A*a^2 + 2*(d*x + c)*B*a^2 + A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a^2*sin(d*x + c) + 2*B*a^2*tan(d*x + c))/d","A",0
58,1,101,0,0.340290," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),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} + 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)} + 8 \, A a^{2} \sin\left(d x + c\right) + 4 \, B a^{2} \sin\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 + 2*B*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))/d","A",0
59,1,110,0,0.330540," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),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} - 12 \, A a^{2} \sin\left(d x + c\right) - 24 \, B 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 - 12*A*a^2*sin(d*x + c) - 24*B*a^2*sin(d*x + c))/d","A",0
60,1,144,0,0.339362," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),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} - 96 \, B 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 - 96*B*a^2*sin(d*x + c))/d","A",0
61,1,178,0,0.340678," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),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}}{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)/d","A",0
62,1,405,0,0.355224," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{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)} A a^{3} + 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)} B a^{3} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} - 5 \, 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)} - 90 \, 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)} - 120 \, 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 \, d}"," ",0,"1/480*(32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^3 + 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))*B*a^3 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 - 5*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)) - 90*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)) - 120*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
63,1,337,0,0.365431," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{240 \, {\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)} B a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} - 15 \, 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)} - 45 \, 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)} - 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 \, 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)} + 240 \, A a^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(240*(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))*B*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 - 15*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)) - 45*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)) - 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*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)) + 240*A*a^3*tan(d*x + c))/d","B",0
64,1,262,0,0.366851," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} - 3 \, 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)} - 36 \, 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)} + 48 \, A 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) + 48 \, B a^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 - 3*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)) - 36*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)) + 48*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 144*A*a^3*tan(d*x + c) + 48*B*a^3*tan(d*x + c))/d","B",0
65,1,198,0,0.359064," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\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)} B a^{3} - 3 \, 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)} - 9 \, 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 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, B a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 36 \, A a^{3} \tan\left(d x + c\right) + 36 \, B a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 - 3*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)) - 9*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*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 12*B*a^3*log(sec(d*x + c) + tan(d*x + c)) + 36*A*a^3*tan(d*x + c) + 36*B*a^3*tan(d*x + c))/d","A",0
66,1,165,0,0.355651," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a^{3} + 4 \, {\left(d x + c\right)} B a^{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)} + 6 \, 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)} + 4 \, A a^{3} \sin\left(d x + c\right) + 4 \, A a^{3} \tan\left(d x + c\right) + 12 \, B a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*A*a^3 + 4*(d*x + c)*B*a^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)) + 6*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)) + 4*A*a^3*sin(d*x + c) + 4*A*a^3*tan(d*x + c) + 12*B*a^3*tan(d*x + c))/d","A",0
67,1,140,0,0.355123," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),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} + 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)} + 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)}{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 + 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)) + 12*A*a^3*sin(d*x + c) + 4*B*a^3*sin(d*x + c) + 4*B*a^3*tan(d*x + c))/d","A",0
68,1,148,0,0.358685," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),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} - 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)} - 36 \, A a^{3} \sin\left(d x + c\right) - 36 \, B a^{3} \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 - 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 - 6*B*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))/d","A",0
69,1,167,0,0.361042," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),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} - 96 \, A a^{3} \sin\left(d x + c\right) - 288 \, B 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 - 96*A*a^3*sin(d*x + c) - 288*B*a^3*sin(d*x + c))/d","A",0
70,1,213,0,0.361203," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),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} + 480 \, B 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 + 480*B*a^3*sin(d*x + c))/d","A",0
71,1,262,0,0.352435," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),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 \, 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)/d","A",0
72,1,464,0,0.352343," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{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)} A a^{4} + 960 \, {\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)} B a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} - 5 \, 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)} - 120 \, 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 \, 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)} - 480 \, 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 \, 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)} + 480 \, A a^{4} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^4 + 960*(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))*B*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 - 5*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)) - 120*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*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)) - 480*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*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)) + 480*A*a^4*tan(d*x + c))/d","B",0
73,1,369,0,0.348554," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A 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)} B a^{4} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} - 15 \, 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)} - 60 \, 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)} - 360 \, 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)} - 240 \, 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 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 960 \, A a^{4} \tan\left(d x + c\right) + 240 \, B a^{4} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(320*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^4 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 - 15*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)) - 60*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)) - 360*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)) - 240*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*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 960*A*a^4*tan(d*x + c) + 240*B*a^4*tan(d*x + c))/d","B",0
74,1,293,0,0.355057," ","integrate((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 48 \, {\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)} B a^{4} - 3 \, 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)} - 48 \, 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 \, 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)} + 192 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, B a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 288 \, A a^{4} \tan\left(d x + c\right) + 192 \, B a^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 48*(d*x + c)*A*a^4 + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 - 3*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)) - 48*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*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)) + 192*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 48*B*a^4*log(sec(d*x + c) + tan(d*x + c)) + 288*A*a^4*tan(d*x + c) + 192*B*a^4*tan(d*x + c))/d","B",0
75,1,235,0,0.353678," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{48 \, {\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)} B a^{4} + 12 \, {\left(d x + c\right)} B a^{4} - 3 \, 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)} - 12 \, 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)} + 36 \, 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)} + 12 \, A a^{4} \sin\left(d x + c\right) + 48 \, A a^{4} \tan\left(d x + c\right) + 72 \, B a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(48*(d*x + c)*A*a^4 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 12*(d*x + c)*B*a^4 - 3*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)) - 12*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)) + 36*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)) + 12*A*a^4*sin(d*x + c) + 48*A*a^4*tan(d*x + c) + 72*B*a^4*tan(d*x + c))/d","A",0
76,1,199,0,0.354082," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 24 \, {\left(d x + c\right)} A a^{4} + 16 \, {\left(d x + c\right)} B a^{4} - 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)} + 8 \, 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)} + 12 \, 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)} + 16 \, A a^{4} \sin\left(d x + c\right) + 4 \, B a^{4} \sin\left(d x + c\right) + 4 \, A a^{4} \tan\left(d x + c\right) + 16 \, B a^{4} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 24*(d*x + c)*A*a^4 + 16*(d*x + c)*B*a^4 - 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)) + 8*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 16*A*a^4*sin(d*x + c) + 4*B*a^4*sin(d*x + c) + 4*A*a^4*tan(d*x + c) + 16*B*a^4*tan(d*x + c))/d","A",0
77,1,187,0,0.352506," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} - 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)} - 72 \, A a^{4} \sin\left(d x + c\right) - 48 \, B a^{4} \sin\left(d x + c\right) - 12 \, B 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 - 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)) - 72*A*a^4*sin(d*x + c) - 48*B*a^4*sin(d*x + c) - 12*B*a^4*tan(d*x + c))/d","A",0
78,1,205,0,0.351076," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} - 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)} - 384 \, A a^{4} \sin\left(d x + c\right) - 576 \, B a^{4} \sin\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 - 48*B*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))/d","A",0
79,1,236,0,0.353700," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} + 480 \, A a^{4} \sin\left(d x + c\right) + 1920 \, B 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 + 480*A*a^4*sin(d*x + c) + 1920*B*a^4*sin(d*x + c))/d","A",0
80,1,297,0,0.352728," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} + 960 \, B 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 + 960*B*a^4*sin(d*x + c))/d","A",0
81,1,356,0,0.349548," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),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}}{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)/d","A",0
82,1,368,0,0.344760," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{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)} - 3 \, 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)}}{6 \, d}"," ",0,"1/6*(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))) - 3*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
83,1,282,0,0.343972," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} + 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{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*(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))) + 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 - 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
84,1,196,0,0.345411," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} - 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)}}{d}"," ",0,"-(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))) - 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
85,1,99,0,0.347167," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{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,"(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
86,1,73,0,0.425014," ","integrate((A+B*sec(d*x+c))/(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)} + \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))) + B*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
87,1,143,0,0.433615," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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)}}{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))))/d","B",0
88,1,225,0,0.445769," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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)}}{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))))/d","B",0
89,1,310,0,0.448313," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(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 \, 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))))/d","B",0
90,1,425,0,0.355897," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(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{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{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)}}{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 - 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*(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))/d","B",0
91,1,336,0,0.355935," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(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{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*(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
92,1,244,0,0.344258," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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{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*(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
93,1,145,0,0.351356," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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{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*(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","A",0
94,1,93,0,0.343525," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\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*(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","A",0
95,1,120,0,0.435532," ","integrate((A+B*sec(d*x+c))/(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{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) - 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
96,1,191,0,0.436003," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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)}}{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))/d","B",0
97,1,283,0,0.444507," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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)}}{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))))/d","B",0
98,1,372,0,0.450019," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(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)}}{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))/d","B",0
99,1,377,0,0.358820," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(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{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 \, 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{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*(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 - 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*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 - 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
100,1,286,0,0.349780," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(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{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*(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","A",0
101,1,187,0,0.340250," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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{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*(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","A",0
102,1,115,0,0.332171," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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 \, 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*(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
103,1,115,0,0.328844," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\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*(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
104,1,160,0,0.421097," ","integrate((A+B*sec(d*x+c))/(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}}}{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)/d","A",0
105,1,231,0,0.437305," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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)}}{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))/d","A",0
106,1,322,0,0.434668," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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)}}{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))/d","A",0
107,1,412,0,0.449991," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(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)}}{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))/d","B",0
108,1,419,0,0.356617," ","integrate(sec(d*x+c)^6*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, B {\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)} - 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{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)}}{840 \, d}"," ",0,"-1/840*(3*B*(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) - 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 - 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))/d","A",0
109,1,326,0,0.357020," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{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*(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","A",0
110,1,228,0,0.361232," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{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*(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","A",0
111,1,175,0,0.357036," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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 \, 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*(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
112,1,174,0,0.356606," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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}}}{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)/d","A",0
113,1,175,0,0.352481," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(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{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*(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
114,1,201,0,0.715126," ","integrate((A+B*sec(d*x+c))/(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{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) - 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
115,1,271,0,0.707880," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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)}}{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))/d","A",0
116,1,364,0,0.710722," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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)}}{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))/d","A",0
117,1,452,0,0.457585," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(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)} - 3 \, B {\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)}}{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) - 3*B*(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))/d","A",0
118,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,1,147,0,0.501572," ","integrate((a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{A \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,"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)*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
123,1,939,0,0.644331," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),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
124,1,1851,0,0.772189," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),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)} 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*((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
125,1,2981,0,1.004192," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),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}{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)/d","B",0
126,1,8561,0,1.423847," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, {\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 - \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*(8*(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 - (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
127,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,1,998,0,0.642179," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),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)} A}{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))*A/((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
131,1,1801,0,0.835468," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),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
132,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,1,1396,0,1.006631," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),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)} A}{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))*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
139,1,2780,0,1.298197," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),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
140,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
145,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
146,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
147,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
148,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
149,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
150,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
151,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
152,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^4/(a*sec(d*x + c) + a)^(3/2), x)","F",0
153,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\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((B*sec(d*x + c) + A)*sec(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
154,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + 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((B*sec(d*x + c) + A)*sec(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
156,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
157,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
158,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
159,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
160,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
164,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
165,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
167,-2,0,0,0.000000," ","integrate((A+A*sec(d*x+c))/(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
168,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)/sqrt(-a*sec(d*x + c) + a), x)","F",0
169,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(-a*sec(d*x + c) + a), x)","F",0
170,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)^3/sqrt(-a*sec(d*x + c) + a), x)","F",0
171,0,0,0,0.000000," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{A \sec\left(d x + c\right) + A}{{\left(-a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((A*sec(d*x + c) + A)/(-a*sec(d*x + c) + a)^(3/2), x)","F",0
172,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)/(-a*sec(d*x + c) + a)^(3/2), x)","F",0
173,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)^2/(-a*sec(d*x + c) + a)^(3/2), x)","F",0
174,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)^3/(-a*sec(d*x + c) + a)^(3/2), x)","F",0
175,0,0,0,0.000000," ","integrate((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{A \sec\left(d x + c\right) + A}{{\left(-a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((A*sec(d*x + c) + A)/(-a*sec(d*x + c) + a)^(5/2), x)","F",0
176,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)/(-a*sec(d*x + c) + a)^(5/2), x)","F",0
177,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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((A*sec(d*x + c) + A)*cos(d*x + c)^2/(-a*sec(d*x + c) + a)^(5/2), x)","F",0
178,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(A \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{5}{2}}}\,{d x}"," ",0,"integrate((A*sec(d*x + c) + A)*cos(d*x + c)^3/(-a*sec(d*x + c) + a)^(5/2), x)","F",0
179,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
180,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
182,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
183,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
185,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
186,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
188,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
189,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
190,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(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{9}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sec(d*x + c)^(9/2), x)","F",0
193,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
195,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
196,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
197,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
198,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
199,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
202,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
203,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
204,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
205,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
206,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
207,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
208,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
209,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*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
213,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
214,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
215,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
216,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*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
221,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
222,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
223,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
224,1,3342,0,2.227190," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}{96 \, d}"," ",0,"-1/96*(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))))*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) + (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))/d","B",0
225,1,1927,0,1.712730," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}{16 \, d}"," ",0,"-1/16*(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))))*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) + (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))/d","B",0
226,1,905,0,1.592619," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, 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(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}}{4 \, d}"," ",0,"1/4*(2*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*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))/d","B",0
227,1,262,0,1.202079," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 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)}}{2 \, d}"," ",0,"1/2*(4*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) + 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)))/d","B",0
228,1,134,0,1.268257," ","integrate((A+B*sec(d*x+c))*(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)}{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))/d","A",0
229,1,317,0,1.260071," ","integrate((A+B*sec(d*x+c))*(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}}{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))/d","B",0
230,1,498,0,1.320385," ","integrate((A+B*sec(d*x+c))*(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}}{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))/d","B",0
231,1,5879,0,2.615449," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\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)} 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{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)} B \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*(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))))*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) + 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))))*B*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
232,1,4606,0,1.952797," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}{96 \, d}"," ",0,"-1/96*(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))))*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) + (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))/d","B",0
233,1,3389,0,1.522083," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\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)} 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(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}}{16 \, d}"," ",0,"1/16*(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))*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) - (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))/d","B",0
234,1,1417,0,1.304098," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\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(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}}{4 \, d}"," ",0,"1/4*(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) + (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))/d","B",0
235,1,314,0,1.528486," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/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}}{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))/d","B",0
236,1,250,0,1.498958," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/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} + 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) + 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
237,1,514,0,1.272949," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/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}}{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))/d","B",0
238,1,700,0,1.345062," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/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}}{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))/d","B",0
239,1,9242,0,5.200795," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{10 \, {\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(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)} B \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*(10*(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) + (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))))*B*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
240,1,7331,0,3.092490," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, {\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(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)} B \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*(8*(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) - (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))))*B*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
241,1,6297,0,8.720664," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{6 \, {\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(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)} B \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}}{96 \, d}"," ",0,"-1/96*(6*(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) - (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))))*B*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))/d","B",0
242,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,1,655,0,1.657859," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{5 \, \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)} B \sqrt{a} + 2 \, {\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}}{60 \, d}"," ",0,"1/60*(5*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))))*B*sqrt(a) + 2*(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))/d","B",0
245,1,385,0,1.394640," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/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} + 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) + 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
246,1,746,0,1.491786," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/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}}{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))/d","B",0
247,1,945,0,1.506871," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/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}}{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))/d","B",0
248,1,2524,0,1.638756," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}}{16 \, d}"," ",0,"-1/16*(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))))*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)) - (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)))/d","B",0
249,1,1353,0,1.555488," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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}{\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}{{\left(\cos\left(2 \, d x + 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*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)*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)))/d","B",0
250,1,567,0,1.576287," ","integrate((A+B*sec(d*x+c))*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)\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)} 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))*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))*B/sqrt(a))/d","B",0
251,1,195,0,1.359036," ","integrate((A+B*sec(d*x+c))/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}}}{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))/d","B",0
252,1,387,0,1.228572," ","integrate((A+B*sec(d*x+c))/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}}}{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))/d","B",0
253,1,640,0,1.389795," ","integrate((A+B*sec(d*x+c))/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}}}{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))/d","B",0
254,1,805,0,2.129057," ","integrate((A+B*sec(d*x+c))/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}}}{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))/d","B",0
255,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,1,7057,0,4.027294," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\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)} A}{{\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}} - \frac{{\left(12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right) + 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 \, \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) - 8 \, {\left(\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{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) + 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) - 12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 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) + 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) - 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) + 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) - 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) - 9 \, {\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} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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(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 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 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) + 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} + 4 \, \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) + 9 \, {\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} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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(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 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 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) + 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} + 4 \, \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) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 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 \, \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) + 8 \, {\left(\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{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) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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) - 24 \, \cos\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) + 2 \, \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) + 24 \, \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)} B}{{\left(\sqrt{2} a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \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} + 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(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \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} + 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} + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(\sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + \sqrt{2} a\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) + 4 \, {\left(\sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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)\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) + 4 \, {\left(\sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a \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) + \sqrt{2} a\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*((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))))*A/((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)) - (12*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 2*sin(3/2*arctan2(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))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8*(sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 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))) + 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 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))) - 4*(sin(4*d*x + 4*c) + 2*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))) - 12*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) - 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) + 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) - 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) - 9*(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 + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 2*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))) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(cos(4*d*x + 4*c) + 2*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(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*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 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))) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sin(4*d*x + 4*c) + 2*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 + 4*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) + 9*(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 + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 2*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))) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(cos(4*d*x + 4*c) + 2*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(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*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 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))) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sin(4*d*x + 4*c) + 2*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 + 4*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) + 2*cos(2*d*x + 2*c) + 2*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(cos(5/4*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))) - 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))) - 4*(cos(4*d*x + 4*c) + 2*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(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*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))) - 24*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) + 2*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 24*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))))*B/((sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(4*d*x + 4*c)^2 + 4*sqrt(2)*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*a*cos(2*d*x + 2*c) + 2*(2*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(4*d*x + 4*c) + 4*(sqrt(2)*a*cos(4*d*x + 4*c) + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 2*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*a*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c) + 2*sqrt(2)*a*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))) + 4*(sqrt(2)*a*sin(4*d*x + 4*c) + 2*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))) + sqrt(2)*a)*sqrt(a)))/d","B",0
257,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*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
259,1,8208,0,1.255330," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 70 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 28 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 4 \, {\left(21 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} - 8 \, {\left(10 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + {\left({\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2\right)} \sin\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(427 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, {\left(61 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + {\left({\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2\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)^{2} + {\left(8 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 259 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 91 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 104 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(37 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, {\left(2 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + {\left(2 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, {\left(84 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, {\left(6 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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} + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\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(147 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, {\left(3 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(2 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + {\left(35 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 40 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} - 4 \, {\left(18 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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} - 4 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 36 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, {\left({\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(18 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(133 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, {\left(21 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} - 8 \, {\left(19 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 80 \, \cos\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) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 11 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a}}{4 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 28 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} \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)^{4} + 4 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 12 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, \sqrt{2} a^{2} \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} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + {\left(\sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 6 \, \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) + 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, \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) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(61 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, \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)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 6 \, \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) + 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, \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) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(8 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 28 \, \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) + 37 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, \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)^{2} + 2 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 13 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} \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)^{3} + \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} + {\left(2 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, {\left(12 \, \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) + 2 \, {\left(2 \, \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) + \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(21 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, \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}\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, \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) \sin\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)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{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) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 6 \, \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) + 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 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(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, \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) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, \sqrt{2} a^{2} \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) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)} - \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)} B}{{\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}}}{4 \, d}"," ",0,"-1/4*((4*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^4 + 63*(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(1/2*d*x + 1/2*c)^4 + 4*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^4 + 70*(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(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^4 - 8*sin(1/2*d*x + 1/2*c)^5 + 28*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^3 + 4*(21*(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(1/2*d*x + 1/2*c) - 24*sin(1/2*d*x + 1/2*c)^2 - 20)*sin(3/2*d*x + 3/2*c)^3 - 8*(10*cos(1/2*d*x + 1/2*c)^2 + 3)*sin(1/2*d*x + 1/2*c)^3 + ((7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(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(1/2*d*x + 1/2*c)^2 + (7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^2 + 2)*sin(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c)^2 + (427*(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(1/2*d*x + 1/2*c)^2 + 35*(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(1/2*d*x + 1/2*c)^2 - 40*sin(1/2*d*x + 1/2*c)^3 - 8*(61*cos(1/2*d*x + 1/2*c)^2 + 9)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + ((7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(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(1/2*d*x + 1/2*c)^2 + (7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^2 + 2)*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)^2 + (8*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 259*(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(1/2*d*x + 1/2*c)^2 + 91*(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(1/2*d*x + 1/2*c)^2 - 104*sin(1/2*d*x + 1/2*c)^3 + 28*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 8*(37*cos(1/2*d*x + 1/2*c)^2 + 21)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(2*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^3 + 63*(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(1/2*d*x + 1/2*c)^3 + 7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^3 + 13*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + (2*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(84*(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(1/2*d*x + 1/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 - 16*(6*cos(1/2*d*x + 1/2*c)^2 + 1)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 2*(7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*cos(3/2*d*x + 3/2*c) - 8*cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^3 + 2*cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(147*(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(1/2*d*x + 1/2*c)^3 + 35*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 40*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^3 - 56*(3*cos(1/2*d*x + 1/2*c)^3 + cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(2*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^3 + 63*(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(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 7*(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(1/2*d*x + 1/2*c)^3 - 8*sin(1/2*d*x + 1/2*c)^4 + (7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 4)*cos(3/2*d*x + 3/2*c)^2 + (35*(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(1/2*d*x + 1/2*c) - 40*sin(1/2*d*x + 1/2*c)^2 - 36)*sin(3/2*d*x + 3/2*c)^2 - 4*(18*cos(1/2*d*x + 1/2*c)^2 + 5)*sin(1/2*d*x + 1/2*c)^2 + 6*(7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 4*cos(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 36*cos(1/2*d*x + 1/2*c)^2 + 2*((7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(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(1/2*d*x + 1/2*c)^2 + 14*(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(1/2*d*x + 1/2*c)^2 - 16*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 4*(18*cos(1/2*d*x + 1/2*c)^2 + 7)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c))*sin(5/2*d*x + 5/2*c) + 2*(133*(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(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 21*(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(1/2*d*x + 1/2*c)^3 - 24*sin(1/2*d*x + 1/2*c)^4 + 2*(21*(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(1/2*d*x + 1/2*c) - 24*sin(1/2*d*x + 1/2*c)^2 - 20)*cos(3/2*d*x + 3/2*c)^2 - 8*(19*cos(1/2*d*x + 1/2*c)^2 + 7)*sin(1/2*d*x + 1/2*c)^2 + 16*(7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 5*cos(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 80*cos(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^4 + 11*cos(1/2*d*x + 1/2*c)^2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a)/(4*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^4 + 28*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^3*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^4 + 4*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^4 + 12*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^3*sin(1/2*d*x + 1/2*c) + 10*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^4 + (sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2 + 2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(5/2*d*x + 5/2*c)^2 + (61*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2 + 2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(5/2*d*x + 5/2*c)^2 + (8*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 28*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 37*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 13*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c)^2 + 2*(2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^3 + 13*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + (2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(12*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) + 2*(2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c))*cos(5/2*d*x + 5/2*c) + 2*(21*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c) + 2*(2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^3 + sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 + 2*(sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*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)^2)*sin(3/2*d*x + 3/2*c))*sin(5/2*d*x + 5/2*c) + 2*(6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + 16*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 19*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 3*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3)*sin(3/2*d*x + 3/2*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) - 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))*B/((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)))/d","B",0
260,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
261,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
262,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,1,5924,0,2.729223," ","integrate((A+B*sec(d*x+c))*sec(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}}}{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)))/d","B",0
266,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
267,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
268,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
269,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
270,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
271,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(4/3), x)","F",0
272,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(4/3), x)","F",0
273,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^(1/3), x)","F",0
274,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(a*sec(d*x + c) + a)^(2/3), x)","F",0
275,0,0,0,0.000000," ","integrate((c*sec(f*x+e))^n*(a+a*sec(f*x+e))^m*(A+B*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sec\left(f x + e\right) + A\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(c \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sec(f*x + e) + A)*(a*sec(f*x + e) + a)^m*(c*sec(f*x + e))^n, x)","F",0
276,0,0,0,0.000000," ","integrate(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^n*sec(d*x + c)^(-n - 1), x)","F",0
277,1,163,0,0.880335," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),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)} A b - 3 \, 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)} - 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 \, 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))*A*b - 3*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)) - 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)))/d","A",0
278,1,127,0,0.657152," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b - 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 \, 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 \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b - 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*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*tan(d*x + c))/d","A",0
279,1,88,0,0.612892," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} - 4 \, A 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 \, A b \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(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)) - 4*A*a*log(sec(d*x + c) + tan(d*x + c)) - 4*B*a*tan(d*x + c) - 4*A*b*tan(d*x + c))/d","A",0
280,1,56,0,0.836243," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} A a + B a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + A b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + B b \tan\left(d x + c\right)}{d}"," ",0,"((d*x + c)*A*a + B*a*log(sec(d*x + c) + tan(d*x + c)) + A*b*log(sec(d*x + c) + tan(d*x + c)) + B*b*tan(d*x + c))/d","A",0
281,1,58,0,0.444680," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + 2 \, {\left(d x + c\right)} A b + 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 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + 2*(d*x + c)*A*b + B*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a*sin(d*x + c))/d","A",0
282,1,55,0,0.780767," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),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 b + 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)*B*b + 4*B*a*sin(d*x + c) + 4*A*b*sin(d*x + c))/d","A",0
283,1,79,0,0.905429," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),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 \, 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*B*b*sin(d*x + c))/d","A",0
284,1,101,0,2.050578," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),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 - 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 \, 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 - 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)/d","A",0
285,1,276,0,0.666614," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \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)} A 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)} B b^{2} - 30 \, B 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 \, 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 \, 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)}}{240 \, d}"," ",0,"1/240*(80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*b^2 - 30*B*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*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*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","A",0
286,1,228,0,0.957754," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{2} - 3 \, 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)} - 12 \, 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)} - 24 \, 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)} + 48 \, 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))*B*a*b + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^2 - 3*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)) - 12*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)) - 24*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)) + 48*A*a^2*tan(d*x + c))/d","A",0
287,1,165,0,1.656962," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{2} - 6 \, 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)} - 3 \, 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 a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, B a^{2} \tan\left(d x + c\right) + 24 \, A a b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^2 - 6*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)) - 3*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*a^2*log(sec(d*x + c) + tan(d*x + c)) + 12*B*a^2*tan(d*x + c) + 24*A*a*b*tan(d*x + c))/d","A",0
288,1,126,0,1.389755," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{2} - 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)} + 4 \, B a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 8 \, A a b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 8 \, B a b \tan\left(d x + c\right) + 4 \, A b^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a^2 - 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)) + 4*B*a^2*log(sec(d*x + c) + tan(d*x + c)) + 8*A*a*b*log(sec(d*x + c) + tan(d*x + c)) + 8*B*a*b*tan(d*x + c) + 4*A*b^2*tan(d*x + c))/d","A",0
289,1,103,0,0.907968," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a^{2} + 4 \, {\left(d x + c\right)} A a b + 2 \, 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)} + 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 a^{2} \sin\left(d x + c\right) + 2 \, B b^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a^2 + 4*(d*x + c)*A*a*b + 2*B*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + A*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*a^2*sin(d*x + c) + 2*B*b^2*tan(d*x + c))/d","A",0
290,1,99,0,0.882649," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 8 \, {\left(d x + c\right)} B a b + 4 \, {\left(d x + c\right)} A b^{2} + 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 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 8*(d*x + c)*B*a*b + 4*(d*x + c)*A*b^2 + 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))/d","A",0
291,1,108,0,1.170808," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),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 - 12 \, {\left(d x + c\right)} B b^{2} - 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 - 12*(d*x + c)*B*b^2 - 24*B*a*b*sin(d*x + c) - 12*A*b^2*sin(d*x + c))/d","A",0
292,1,142,0,1.674117," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),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} - 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 \, 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 - 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*B*b^2*sin(d*x + c))/d","A",0
293,1,176,0,0.959953," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),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} + 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 - 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 \, 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 + 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 - 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)/d","A",0
294,1,341,0,0.826931," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A 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)} B b^{3} - 45 \, 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)} - 15 \, 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 \, 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)} - 180 \, 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)} + 240 \, A 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^2*b + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^2 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*b^3 - 45*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)) - 15*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*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)) - 180*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)) + 240*A*a^3*tan(d*x + c))/d","A",0
295,1,266,0,0.740975," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{2} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{3} - 3 \, 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)} - 36 \, 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)} - 36 \, 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)} + 48 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 48 \, B a^{3} \tan\left(d x + c\right) + 144 \, A 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))*B*a*b^2 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^3 - 3*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)) - 36*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)) - 36*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)) + 48*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 48*B*a^3*tan(d*x + c) + 144*A*a^2*b*tan(d*x + c))/d","A",0
296,1,202,0,0.324716," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\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)} B b^{3} - 9 \, 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)} - 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 \, B a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 36 \, A a^{2} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 36 \, B a^{2} b \tan\left(d x + c\right) + 36 \, A a b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^3 - 9*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)) - 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*B*a^3*log(sec(d*x + c) + tan(d*x + c)) + 36*A*a^2*b*log(sec(d*x + c) + tan(d*x + c)) + 36*B*a^2*b*tan(d*x + c) + 36*A*a*b^2*tan(d*x + c))/d","A",0
297,1,169,0,0.766288," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{3} + 12 \, {\left(d x + c\right)} A a^{2} b - 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 \, 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)} + 6 \, 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)} + 4 \, A a^{3} \sin\left(d x + c\right) + 12 \, B a b^{2} \tan\left(d x + c\right) + 4 \, A b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a^3 + 12*(d*x + c)*A*a^2*b - 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*B*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*A*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a^3*sin(d*x + c) + 12*B*a*b^2*tan(d*x + c) + 4*A*b^3*tan(d*x + c))/d","A",0
298,1,144,0,0.809689," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),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)} B a^{2} b + 12 \, {\left(d x + c\right)} A a b^{2} + 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) + 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 + 12*(d*x + c)*B*a^2*b + 12*(d*x + c)*A*a*b^2 + 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) + 4*B*b^3*tan(d*x + c))/d","A",0
299,1,152,0,0.696317," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),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)} B a b^{2} - 12 \, {\left(d x + c\right)} A b^{3} - 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)} - 36 \, B a^{2} b \sin\left(d x + c\right) - 36 \, A 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^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)*B*a*b^2 - 12*(d*x + c)*A*b^3 - 6*B*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*B*a^2*b*sin(d*x + c) - 36*A*a*b^2*sin(d*x + c))/d","A",0
300,1,171,0,0.670007," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),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} - 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} + 96 \, {\left(d x + c\right)} B b^{3} + 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 - 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 + 96*(d*x + c)*B*b^3 + 288*B*a*b^2*sin(d*x + c) + 96*A*b^3*sin(d*x + c))/d","A",0
301,1,217,0,0.681677," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),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} + 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 - 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 \, 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 + 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 - 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*B*b^3*sin(d*x + c))/d","A",0
302,1,474,0,0.763550," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} b + 960 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 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)} B 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)} A b^{4} - 5 \, 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)} - 180 \, 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)} - 120 \, 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)} - 120 \, 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)} - 480 \, 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)} + 480 \, 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))*B*a^3*b + 960*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b^2 + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a*b^3 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*b^4 - 5*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)) - 180*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)) - 120*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)) - 120*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)) - 480*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)) + 480*A*a^4*tan(d*x + c))/d","A",0
303,1,379,0,1.019255," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b^{2} + 320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A 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)} B b^{4} - 60 \, 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)} - 15 \, 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)} - 240 \, 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)} - 360 \, 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)} + 240 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 240 \, B a^{4} \tan\left(d x + c\right) + 960 \, A a^{3} b \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b^2 + 320*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^3 + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*b^4 - 60*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)) - 15*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)) - 240*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)) - 360*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)) + 240*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 240*B*a^4*tan(d*x + c) + 960*A*a^3*b*tan(d*x + c))/d","A",0
304,1,303,0,0.839360," ","integrate((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{48 \, {\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)} B a b^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{4} - 3 \, 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)} - 72 \, 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)} - 48 \, 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)} + 48 \, B a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 192 \, A a^{3} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 192 \, B a^{3} b \tan\left(d x + c\right) + 288 \, A a^{2} b^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(d*x + c)*A*a^4 + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^4 - 3*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)) - 72*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)) - 48*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)) + 48*B*a^4*log(sec(d*x + c) + tan(d*x + c)) + 192*A*a^3*b*log(sec(d*x + c) + tan(d*x + c)) + 192*B*a^3*b*tan(d*x + c) + 288*A*a^2*b^2*tan(d*x + c))/d","A",0
305,1,245,0,0.627434," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{4} + 48 \, {\left(d x + c\right)} A a^{3} b + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b^{4} - 12 \, 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)} - 3 \, 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 \, 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)} + 36 \, 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)} + 12 \, A a^{4} \sin\left(d x + c\right) + 72 \, B a^{2} b^{2} \tan\left(d x + c\right) + 48 \, A a b^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*B*a^4 + 48*(d*x + c)*A*a^3*b + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b^4 - 12*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)) - 3*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*B*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*A*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^4*sin(d*x + c) + 72*B*a^2*b^2*tan(d*x + c) + 48*A*a*b^3*tan(d*x + c))/d","A",0
306,1,209,0,0.719369," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 16 \, {\left(d x + c\right)} B a^{3} b + 24 \, {\left(d x + c\right)} A a^{2} b^{2} - 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)} + 12 \, 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)} + 8 \, 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)} + 4 \, B a^{4} \sin\left(d x + c\right) + 16 \, A a^{3} b \sin\left(d x + c\right) + 16 \, B a b^{3} \tan\left(d x + c\right) + 4 \, A b^{4} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 16*(d*x + c)*B*a^3*b + 24*(d*x + c)*A*a^2*b^2 - 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)) + 12*B*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*A*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^4*sin(d*x + c) + 16*A*a^3*b*sin(d*x + c) + 16*B*a*b^3*tan(d*x + c) + 4*A*b^4*tan(d*x + c))/d","A",0
307,1,197,0,0.722949," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),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 - 72 \, {\left(d x + c\right)} B a^{2} b^{2} - 48 \, {\left(d x + c\right)} A a b^{3} - 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)} - 48 \, B a^{3} b \sin\left(d x + c\right) - 72 \, A a^{2} b^{2} \sin\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 - 72*(d*x + c)*B*a^2*b^2 - 48*(d*x + c)*A*a*b^3 - 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)) - 48*B*a^3*b*sin(d*x + c) - 72*A*a^2*b^2*sin(d*x + c) - 12*B*b^4*tan(d*x + c))/d","A",0
308,1,215,0,0.702722," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} - 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} + 384 \, {\left(d x + c\right)} B a b^{3} + 96 \, {\left(d x + c\right)} A b^{4} + 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)} + 576 \, B a^{2} b^{2} \sin\left(d x + c\right) + 384 \, A 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^4 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*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 + 384*(d*x + c)*B*a*b^3 + 96*(d*x + c)*A*b^4 + 48*B*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 576*B*a^2*b^2*sin(d*x + c) + 384*A*a*b^3*sin(d*x + c))/d","A",0
309,1,246,0,0.745841," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} + 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 - 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} + 480 \, {\left(d x + c\right)} B b^{4} + 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 + 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 - 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 + 480*(d*x + c)*B*b^4 + 1920*B*a*b^3*sin(d*x + c) + 480*A*b^4*sin(d*x + c))/d","A",0
310,1,307,0,0.867475," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),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} - 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 - 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} + 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 \, 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 - 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 - 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 + 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*B*b^4*sin(d*x + c))/d","A",0
311,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(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
312,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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
313,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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
314,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(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
315,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
316,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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
317,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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
318,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(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
319,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*sec(d*x+c))/(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
320,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(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
321,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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
322,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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
323,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(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
324,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
325,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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
326,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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
327,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(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
328,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(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
329,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(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
330,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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
331,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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
332,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(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
333,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
334,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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
335,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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
336,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5*(A+B*sec(d*x+c))/(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
337,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(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
338,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(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
339,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(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
340,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(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
341,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
342,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(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
343,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(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
344,-2,0,0,0.000000," ","integrate((b*B/a+B*sec(d*x+c))/(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
345,-2,0,0,0.000000," ","integrate((a*B/b+B*sec(d*x+c))/(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
346,-2,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/(b+a*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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
347,1,80,0,1.109226," ","integrate((3+sec(d*x+c))/(2-sec(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, \sqrt{3} \log\left(-\frac{\sqrt{3} - \frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}{\sqrt{3} + \frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right) - 18 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{6 \, d}"," ",0,"-1/6*(5*sqrt(3)*log(-(sqrt(3) - 3*sin(d*x + c)/(cos(d*x + c) + 1))/(sqrt(3) + 3*sin(d*x + c)/(cos(d*x + c) + 1))) - 18*arctan(sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
348,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
351,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
352,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a), x)","F",0
353,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
354,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
355,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
356,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
359,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2), x)","F",0
360,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
361,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
362,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
363,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2), x)","F",0
367,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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)\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
368,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
369,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
370,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
371,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
373,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
374,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/sqrt(b*sec(d*x + c) + a), x)","F",0
375,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
376,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
377,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
378,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
382,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
383,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
384,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^3/(b*sec(d*x + c) + a)^(3/2), x)","F",0
385,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
390,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
391,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*cos(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
392,0,0,0,0.000000," ","integrate(sec(f*x+e)*(A+A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(A \sec\left(f x + e\right) + A\right)} \sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((A*sec(f*x + e) + A)*sec(f*x + e)/sqrt(b*sec(f*x + e) + a), x)","F",0
393,0,0,0,0.000000," ","integrate(sec(f*x+e)*(A-A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(A \sec\left(f x + e\right) - A\right)} \sec\left(f x + e\right)}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"-integrate((A*sec(f*x + e) - A)*sec(f*x + e)/sqrt(b*sec(f*x + e) + a), x)","F",0
394,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
395,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
396,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
399,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
400,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
402,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
403,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
404,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
405,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
406,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
411,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a), x)","F",0
416,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
417,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
418,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
419,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
420,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
421,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
422,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
427,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
428,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
434,-2,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
435,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
436,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
437,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
438,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
440,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
441,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
442,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
443,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
444,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
445,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
446,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
447,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(9/2), x)","F",0
448,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
450,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
451,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
452,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
453,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
454,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
455,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(11/2), x)","F",0
456,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
457,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
458,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
459,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
460,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
461,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
462,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
464,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
465,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
466,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
467,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
468,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
469,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sec\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
470,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
471,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
472,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
473,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
474,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
475,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(1/3), x)","F",0
476,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
477,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
478,0,0,0,0.000000," ","integrate((c*sec(f*x+e))^n*(a+b*sec(f*x+e))^m*(A+B*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sec\left(f x + e\right) + A\right)} {\left(b \sec\left(f x + e\right) + a\right)}^{m} \left(c \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sec(f*x + e) + A)*(b*sec(f*x + e) + a)^m*(c*sec(f*x + e))^n, x)","F",0
479,-1,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \sec\left(d x + c\right) + A\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^3*sec(d*x + c)^m, x)","F",0
481,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sec(d*x + c)^m, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(d*x+c)^m*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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)^{m}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sec(d*x + c)^m, x)","F",0
483,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
484,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
485,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
486,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
487,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
488,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
489,-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)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
491,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
492,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
493,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
494,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
495,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
497,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
498,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
499,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
500,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
501,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
502,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
503,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
504,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
505,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
506,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
507,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
508,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
509,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
510,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
511,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
512,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
513,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
514,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
515,1,547,0,0.755397," ","integrate(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c))*(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}}{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))/d","B",0
516,1,418,0,0.790854," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(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}}{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))/d","B",0
517,1,296,0,0.837508," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(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} - 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) - 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
518,1,141,0,0.663327," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(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)}{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))))/d","B",0
519,1,262,0,0.639529," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{4 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 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)}}{2 \, d}"," ",0,"1/2*(4*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) + 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)))/d","B",0
520,1,905,0,0.864206," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, 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(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}}{4 \, d}"," ",0,"1/4*(2*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*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))/d","B",0
521,1,1927,0,0.829411," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}{16 \, d}"," ",0,"-1/16*(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))))*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) + (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))/d","B",0
522,1,3342,0,1.231533," ","integrate((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}{96 \, d}"," ",0,"-1/96*(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))))*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) + (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))/d","B",0
523,1,703,0,0.763231," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
524,1,558,0,0.697886," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
525,1,451,0,0.721575," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
526,1,276,0,0.681786," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
527,1,583,0,0.863948," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{10 \, {\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} + 3 \, {\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}}{30 \, d}"," ",0,"1/30*(10*(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*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))/d","B",0
528,1,1417,0,0.802470," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\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(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}}{4 \, d}"," ",0,"1/4*(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) + (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))/d","B",0
529,1,3389,0,0.896288," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\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)} 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(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}}{16 \, d}"," ",0,"1/16*(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))*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) - (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))/d","B",0
530,1,4606,0,1.019937," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}{96 \, d}"," ",0,"-1/96*(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))))*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) + (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))/d","B",0
531,1,5879,0,1.461834," ","integrate((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\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)} 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{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)} B \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*(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))))*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) + 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))))*B*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
532,1,754,0,0.748124," ","integrate(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
533,1,596,0,0.921276," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
534,1,482,0,0.693850," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),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}}{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))/d","B",0
535,1,352,0,0.682688," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\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} + 5 \, {\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}}{30 \, d}"," ",0,"1/30*((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*(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))/d","B",0
536,1,2589,0,0.839946," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\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(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}}}{12 \, d}"," ",0,"1/12*(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*(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))/d","B",0
537,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,1,6297,0,4.676694," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{6 \, {\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(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)} B \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}}{96 \, d}"," ",0,"-1/96*(6*(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) - (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))))*B*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))/d","B",0
539,1,7331,0,1.411279," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\frac{8 \, {\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(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)} B \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*(8*(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) - (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))))*B*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
540,1,9242,0,2.280003," ","integrate((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{10 \, {\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(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)} B \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*(10*(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) + (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))))*B*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
541,1,749,0,0.812235," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(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}}}{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))/d","B",0
542,1,581,0,0.750983," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(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}}}{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))/d","B",0
543,1,478,0,0.703020," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(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}}}{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))/d","B",0
544,1,195,0,0.647541," ","integrate((A+B*sec(d*x+c))*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}{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}}}{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))/d","A",0
545,1,699,0,0.716123," ","integrate((A+B*sec(d*x+c))/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)\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)} 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))*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))*B/sqrt(a))/d","B",0
546,1,1509,0,0.828722," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \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 \, \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}}}{4 \, d}"," ",0,"-1/4*(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/sqrt(a) + (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)))/d","B",0
547,1,2704,0,0.916819," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)} 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(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}}}{16 \, d}"," ",0,"-1/16*(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))))*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)) - (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)))/d","B",0
548,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(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
549,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,1,8208,0,0.940328," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 70 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 28 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 4 \, {\left(21 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} - 8 \, {\left(10 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + {\left({\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2\right)} \sin\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(427 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 35 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, {\left(61 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + {\left({\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2\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)^{2} + {\left(8 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 259 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 91 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 104 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 28 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(37 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, {\left(2 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + {\left(2 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, {\left(84 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, {\left(6 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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} + 2 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\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(147 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 35 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 40 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, {\left(3 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(2 \, {\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + {\left(35 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 40 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} - 4 \, {\left(18 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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} - 4 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 36 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, {\left({\left(7 \, \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) - 7 \, \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) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 63 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 14 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(18 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(133 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, {\left(21 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 20\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} - 8 \, {\left(19 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, {\left(7 \, {\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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \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 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 80 \, \cos\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) - 8 \, {\left(9 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 11 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a}}{4 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 28 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} \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)^{4} + 4 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{4} + 12 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, \sqrt{2} a^{2} \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} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + {\left(\sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 6 \, \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) + 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, \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) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(61 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, \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)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 6 \, \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) + 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, \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) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(8 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 28 \, \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) + 37 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 13 \, \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)^{2} + 2 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + 13 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} \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)^{3} + \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} + {\left(2 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 2 \, {\left(12 \, \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) + 2 \, {\left(2 \, \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) + \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(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(21 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, \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}\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2 \, {\left(2 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{3} + \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, \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) \sin\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)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{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) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} + 6 \, \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) + 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 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(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(6 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, \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) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 19 \, \sqrt{2} a^{2} \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) + 3 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)} - \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)} B}{{\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}}}{4 \, d}"," ",0,"-1/4*((4*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^4 + 63*(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(1/2*d*x + 1/2*c)^4 + 4*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^4 + 70*(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(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^4 - 8*sin(1/2*d*x + 1/2*c)^5 + 28*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^3 + 4*(21*(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(1/2*d*x + 1/2*c) - 24*sin(1/2*d*x + 1/2*c)^2 - 20)*sin(3/2*d*x + 3/2*c)^3 - 8*(10*cos(1/2*d*x + 1/2*c)^2 + 3)*sin(1/2*d*x + 1/2*c)^3 + ((7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(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(1/2*d*x + 1/2*c)^2 + (7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^2 + 2)*sin(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c)^2 + (427*(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(1/2*d*x + 1/2*c)^2 + 35*(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(1/2*d*x + 1/2*c)^2 - 40*sin(1/2*d*x + 1/2*c)^3 - 8*(61*cos(1/2*d*x + 1/2*c)^2 + 9)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + ((7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(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(1/2*d*x + 1/2*c)^2 + (7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^2 + 2)*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)^2 + (8*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 259*(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(1/2*d*x + 1/2*c)^2 + 91*(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(1/2*d*x + 1/2*c)^2 - 104*sin(1/2*d*x + 1/2*c)^3 + 28*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 8*(37*cos(1/2*d*x + 1/2*c)^2 + 21)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(2*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^3 + 63*(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(1/2*d*x + 1/2*c)^3 + 7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^3 + 13*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + (2*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(84*(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(1/2*d*x + 1/2*c)^2 + 7*(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(1/2*d*x + 1/2*c)^2 - 8*sin(1/2*d*x + 1/2*c)^3 - 16*(6*cos(1/2*d*x + 1/2*c)^2 + 1)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 2*(7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 8)*cos(3/2*d*x + 3/2*c) - 8*cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^3 + 2*cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(147*(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(1/2*d*x + 1/2*c)^3 + 35*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 40*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^3 - 56*(3*cos(1/2*d*x + 1/2*c)^3 + cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) + 2*(2*(7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^3 + 63*(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(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 7*(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(1/2*d*x + 1/2*c)^3 - 8*sin(1/2*d*x + 1/2*c)^4 + (7*(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(1/2*d*x + 1/2*c) - 8*sin(1/2*d*x + 1/2*c)^2 - 4)*cos(3/2*d*x + 3/2*c)^2 + (35*(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(1/2*d*x + 1/2*c) - 40*sin(1/2*d*x + 1/2*c)^2 - 36)*sin(3/2*d*x + 3/2*c)^2 - 4*(18*cos(1/2*d*x + 1/2*c)^2 + 5)*sin(1/2*d*x + 1/2*c)^2 + 6*(7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 4*cos(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 36*cos(1/2*d*x + 1/2*c)^2 + 2*((7*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) - 7*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) - 8*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c)^2 + 63*(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(1/2*d*x + 1/2*c)^2 + 14*(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(1/2*d*x + 1/2*c)^2 - 16*sin(1/2*d*x + 1/2*c)^3 + 6*(7*(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(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 4*(18*cos(1/2*d*x + 1/2*c)^2 + 7)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c))*sin(5/2*d*x + 5/2*c) + 2*(133*(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(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 21*(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(1/2*d*x + 1/2*c)^3 - 24*sin(1/2*d*x + 1/2*c)^4 + 2*(21*(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(1/2*d*x + 1/2*c) - 24*sin(1/2*d*x + 1/2*c)^2 - 20)*cos(3/2*d*x + 3/2*c)^2 - 8*(19*cos(1/2*d*x + 1/2*c)^2 + 7)*sin(1/2*d*x + 1/2*c)^2 + 16*(7*(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(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) - 8*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 - 5*cos(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - 80*cos(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) - 8*(9*cos(1/2*d*x + 1/2*c)^4 + 11*cos(1/2*d*x + 1/2*c)^2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a)/(4*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^4 + 28*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^3*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^4 + 4*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^4 + 12*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^3*sin(1/2*d*x + 1/2*c) + 10*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^4 + (sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2 + 2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(5/2*d*x + 5/2*c)^2 + (61*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 5*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c)^2 + (sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2 + 2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(5/2*d*x + 5/2*c)^2 + (8*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 28*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 37*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 13*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c)^2 + 2*(2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^3 + 13*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*cos(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + (2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)^2 + 2*(12*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) + 2*(2*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c))*cos(5/2*d*x + 5/2*c) + 2*(21*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c) + 2*(2*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^3 + sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 + 2*(sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2 + 6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 9*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)^2)*sin(3/2*d*x + 3/2*c))*sin(5/2*d*x + 5/2*c) + 2*(6*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)^2*sin(1/2*d*x + 1/2*c) + 16*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 19*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2*sin(1/2*d*x + 1/2*c) + 3*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3)*sin(3/2*d*x + 3/2*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) - 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))*B/((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)))/d","B",0
551,1,2166,0,0.826436," ","integrate((A+B*sec(d*x+c))/(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(\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}}}{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)))/d","B",0
552,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
553,1,7057,0,1.434520," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\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)} A}{{\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}} - \frac{{\left(12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right) + 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 \, \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) - 8 \, {\left(\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{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) + 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) - 12 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 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) + 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) - 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) + 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) - 3 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \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} + 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(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} + 4 \, \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} + 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} + 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 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 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)} \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 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, \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) - 9 \, {\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} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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(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 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 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) + 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} + 4 \, \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) + 9 \, {\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} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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(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 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \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)} \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{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 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) + 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} + 4 \, \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) + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 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 \, \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) + 8 \, {\left(\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{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) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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) - 24 \, \cos\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) + 2 \, \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) + 24 \, \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)} B}{{\left(\sqrt{2} a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \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} + 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(4 \, d x + 4 \, c\right)^{2} + 4 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \sqrt{2} a \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} + 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} + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(\sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, \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) + \sqrt{2} a\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) + 4 \, {\left(\sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 2 \, \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) + 4 \, {\left(\sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 2 \, \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)\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) + 4 \, {\left(\sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a \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) + \sqrt{2} a\right)} \sqrt{a}}}{4 \, d}"," ",0,"1/4*((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))))*A/((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)) - (12*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 2*sin(3/2*arctan2(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))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 8*(sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 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))) + 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 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))) - 4*(sin(4*d*x + 4*c) + 2*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))) - 12*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) - 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) + 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) - 3*(sqrt(2)*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(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 + 4*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(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(4*d*x + 4*c) + 2*sqrt(2)*cos(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c) + 2*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))) + 4*(sqrt(2)*sin(4*d*x + 4*c) + 2*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)*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) - 9*(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 + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 2*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))) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(cos(4*d*x + 4*c) + 2*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(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*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 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))) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sin(4*d*x + 4*c) + 2*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 + 4*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) + 9*(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 + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 2*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))) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(cos(4*d*x + 4*c) + 2*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(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*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c) + 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))) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*(sin(4*d*x + 4*c) + 2*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 + 4*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) + 2*cos(2*d*x + 2*c) + 2*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(cos(5/4*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))) - 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))) - 4*(cos(4*d*x + 4*c) + 2*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(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*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))) - 24*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) + 2*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 24*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))))*B/((sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(3/2*arctan2(sin(2*d*x + 2*c), 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(4*d*x + 4*c)^2 + 4*sqrt(2)*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 4*sqrt(2)*a*cos(2*d*x + 2*c) + 2*(2*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(4*d*x + 4*c) + 4*(sqrt(2)*a*cos(4*d*x + 4*c) + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 2*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(sqrt(2)*a*cos(4*d*x + 4*c) + 2*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))) + 4*(sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c) + 2*sqrt(2)*a*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))) + 4*(sqrt(2)*a*sin(4*d*x + 4*c) + 2*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))) + sqrt(2)*a)*sqrt(a)))/d","B",0
554,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*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
558,1,5924,0,1.548700," ","integrate((A+B*sec(d*x+c))/(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(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}}}{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)))/d","B",0
559,1,5356,0,1.239820," ","integrate((A+B*sec(d*x+c))/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(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)} B}{{\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)) - (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))))*B/((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
560,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
561,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
563,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
564,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
565,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
568,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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{7}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
569,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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{5}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
570,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
571,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
573,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
575,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
576,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
577,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
578,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
579,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
580,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
581,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
582,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
583,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
584,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
585,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
586,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*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
589,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(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
590,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
591,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/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
592,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
595,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
596,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
598,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
599,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
600,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(9/2), x)","F",0
601,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
602,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
603,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
604,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
605,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
606,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
607,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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{11}{2}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(11/2), x)","F",0
608,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
609,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
610,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
611,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
614,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*(b*sec(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
615,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
616,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
617,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(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((B*sec(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
618,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
619,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
620,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
621,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),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))*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
624,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
625,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
626,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(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
627,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((A+B*sec(d*x+c))*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
631,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
632,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
633,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
634,0,0,0,0.000000," ","integrate((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sec\left(d x + c\right) + A}{{\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((B*sec(d*x + c) + A)/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2)), x)","F",0
