1,1,95,0,0.776253," ","integrate(sec(d*x+c)^4*(a+a*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 - 3 \, 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)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a - 3*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
2,1,70,0,0.487525," ","integrate(sec(d*x+c)^3*(a+a*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)} a - 3 \, 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 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a - 3*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
3,1,58,0,0.318517," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{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 \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(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*tan(d*x + c))/d","A",0
4,1,29,0,0.631980," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + a \tan\left(d x + c\right)}{d}"," ",0,"(a*log(sec(d*x + c) + tan(d*x + c)) + a*tan(d*x + c))/d","A",0
5,1,23,0,0.654451," ","integrate(a+a*sec(d*x+c),x, algorithm=""maxima"")","a x + \frac{a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d}"," ",0,"a*x + a*log(sec(d*x + c) + tan(d*x + c))/d","A",0
6,1,20,0,0.359143," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a + a \sin\left(d x + c\right)}{d}"," ",0,"((d*x + c)*a + a*sin(d*x + c))/d","A",0
7,1,34,0,0.970462," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a + 4 \, a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a + 4*a*sin(d*x + c))/d","A",0
8,1,46,0,0.324110," ","integrate(cos(d*x+c)^3*(a+a*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 - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a)/d","A",0
9,1,57,0,0.751376," ","integrate(cos(d*x+c)^4*(a+a*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 - 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}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
10,1,133,0,0.340085," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} - 15 \, a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"1/120*(8*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 - 15*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)))/d","A",0
11,1,145,0,0.772335," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} - 3 \, a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{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 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 - 3*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*a^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
12,1,85,0,0.659163," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} - 3 \, 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 \, a^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 - 3*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*a^2*tan(d*x + c))/d","A",0
13,1,81,0,0.645086," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 8 \, a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*a^2*log(sec(d*x + c) + tan(d*x + c)) - 8*a^2*tan(d*x + c))/d","A",0
14,1,41,0,0.477435," ","integrate((a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{2 \, a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{a^{2} \tan\left(d x + c\right)}{d}"," ",0,"a^2*x + 2*a^2*log(sec(d*x + c) + tan(d*x + c))/d + a^2*tan(d*x + c)/d","A",0
15,1,52,0,0.834541," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} a^{2} + 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^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a^2 + a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a^2*sin(d*x + c))/d","A",0
16,1,48,0,0.788005," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} + 4 \, {\left(d x + c\right)} a^{2} + 8 \, 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^2 + 4*(d*x + c)*a^2 + 8*a^2*sin(d*x + c))/d","A",0
17,1,61,0,0.725752," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 6 \, a^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 6*a^2*sin(d*x + c))/d","A",0
18,1,83,0,0.903145," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{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^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{96 \, d}"," ",0,"-1/96*(64*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2)/d","A",0
19,1,95,0,0.657094," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{240 \, d}"," ",0,"1/240*(16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2 - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2)/d","A",0
20,1,179,0,0.821359," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{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)} a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} - 45 \, 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)} - 60 \, 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 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - 45*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)) - 60*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
21,1,156,0,0.620611," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} - a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{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)} + 16 \, a^{3} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 16*a^3*tan(d*x + c))/d","A",0
22,1,104,0,0.318785," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} - 9 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 36 \, a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - 9*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*a^3*log(sec(d*x + c) + tan(d*x + c)) + 36*a^3*tan(d*x + c))/d","A",0
23,1,91,0,0.405719," ","integrate((a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x - \frac{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)}}{4 \, d} + \frac{3 \, a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{3 \, a^{3} \tan\left(d x + c\right)}{d}"," ",0,"a^3*x - 1/4*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 + 3*a^3*log(sec(d*x + c) + tan(d*x + c))/d + 3*a^3*tan(d*x + c)/d","A",0
24,1,64,0,0.739586," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a^{3} + 3 \, a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, a^{3} \sin\left(d x + c\right) + 2 \, a^{3} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(6*(d*x + c)*a^3 + 3*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a^3*sin(d*x + c) + 2*a^3*tan(d*x + c))/d","A",0
25,1,74,0,0.519784," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 12 \, {\left(d x + c\right)} a^{3} + 2 \, 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^{3} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 + 12*(d*x + c)*a^3 + 2*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*a^3*sin(d*x + c))/d","A",0
26,1,71,0,0.583488," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 12 \, {\left(d x + c\right)} a^{3} - 36 \, 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^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 12*(d*x + c)*a^3 - 36*a^3*sin(d*x + c))/d","A",0
27,1,94,0,0.507527," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} 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^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 32 \, a^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"-1/32*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 32*a^3*sin(d*x + c))/d","A",0
28,1,117,0,0.445164," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^3,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^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} 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^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3)/d","A",0
29,1,143,0,0.530155," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^3,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^{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^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} 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^{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^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^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3)/d","A",0
30,1,270,0,0.712252," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{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)} a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} - 5 \, 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)} - 180 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, 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 \, d}"," ",0,"1/480*(128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 - 5*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)) - 180*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*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)))/d","B",0
31,1,190,0,0.687058," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} - 15 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 60 \, a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(4*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 - 15*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 60*a^4*tan(d*x + c))/d","A",0
32,1,175,0,0.539240," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} - 3 \, 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)} - 72 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 192 \, a^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(64*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 - 3*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)) - 72*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*a^4*log(sec(d*x + c) + tan(d*x + c)) + 192*a^4*tan(d*x + c))/d","A",0
33,1,116,0,0.438200," ","integrate((a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4}}{3 \, d} - \frac{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)}}{d} + \frac{4 \, a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{6 \, a^{4} \tan\left(d x + c\right)}{d}"," ",0,"a^4*x + 1/3*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4/d - 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))/d + 4*a^4*log(sec(d*x + c) + tan(d*x + c))/d + 6*a^4*tan(d*x + c)/d","A",0
34,1,110,0,0.633514," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} a^{4} - 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 \, a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, a^{4} \sin\left(d x + c\right) + 16 \, a^{4} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(16*(d*x + c)*a^4 - 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*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*a^4*sin(d*x + c) + 16*a^4*tan(d*x + c))/d","A",0
35,1,85,0,0.352469," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 24 \, {\left(d x + c\right)} a^{4} + 8 \, 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^{4} \sin\left(d x + c\right) + 4 \, 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^4 + 24*(d*x + c)*a^4 + 8*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 16*a^4*sin(d*x + c) + 4*a^4*tan(d*x + c))/d","A",0
36,1,97,0,0.932084," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 24 \, {\left(d x + c\right)} a^{4} - 3 \, a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, a^{4} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 - 24*(d*x + c)*a^4 - 3*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*a^4*sin(d*x + c))/d","A",0
37,1,104,0,0.749489," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} 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^{4} - 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 96 \, {\left(d x + c\right)} a^{4} - 384 \, 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^4 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 - 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 - 96*(d*x + c)*a^4 - 384*a^4*sin(d*x + c))/d","A",0
38,1,128,0,0.448703," ","integrate(cos(d*x+c)^5*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4} - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 120 \, a^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4 - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 + 120*a^4*sin(d*x + c))/d","A",0
39,1,165,0,0.716753," ","integrate(cos(d*x+c)^6*(a+a*sec(d*x+c))^4,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^{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^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} 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^{4} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{960 \, d}"," ",0,"1/960*(256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*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^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4)/d","A",0
40,1,187,0,0.715029," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{48 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{4} - 672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 560 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{1680 \, d}"," ",0,"-1/1680*(48*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^4 - 672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^4 + 560*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4)/d","A",0
41,1,314,0,0.735086," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{96 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{5} + 2240 \, {\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^{5} + 5600 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{5} - 175 \, a^{5} {\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)} - 2100 \, a^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, a^{5} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{3360 \, d}"," ",0,"1/3360*(96*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^5 + 2240*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^5 + 5600*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^5 - 175*a^5*(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)) - 2100*a^5*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*a^5*(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
42,1,205,0,0.651851," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\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)}}}{6 \, d}"," ",0,"1/6*(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)))/d","B",0
43,1,162,0,0.588644," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\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)}}}{2 \, d}"," ",0,"-1/2*(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","A",0
44,1,119,0,0.410635," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\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)}}}{d}"," ",0,"-(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
45,1,75,0,0.666112," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\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)}}}{d}"," ",0,"(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","A",0
46,1,23,0,0.391814," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)}{a d {\left(\cos\left(d x + c\right) + 1\right)}}"," ",0,"sin(d*x + c)/(a*d*(cos(d*x + c) + 1))","A",0
47,1,49,0,1.154342," ","integrate(1/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\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)}}}{d}"," ",0,"(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
48,1,92,0,0.610075," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\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)}}}{d}"," ",0,"-(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
49,1,133,0,0.686088," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\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)}}}{d}"," ",0,"-((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","A",0
50,1,176,0,1.069889," ","integrate(cos(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\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)}}}{3 \, d}"," ",0,"1/3*((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)))/d","A",0
51,1,217,0,1.174357," ","integrate(cos(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{12 \, d}"," ",0,"-1/12*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
52,1,190,0,1.171535," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\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}}}{6 \, d}"," ",0,"-1/6*(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","A",0
53,1,145,0,0.488355," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\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)}}}{6 \, d}"," ",0,"1/6*((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","A",0
54,1,98,0,0.435184," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\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}}}{6 \, d}"," ",0,"-1/6*((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","A",0
55,1,46,0,0.497430," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\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}}}{6 \, a^{2} d}"," ",0,"1/6*(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
56,1,47,0,0.878068," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\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}}}{6 \, a^{2} d}"," ",0,"1/6*(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
57,1,72,0,1.415179," ","integrate(1/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\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}}}{6 \, d}"," ",0,"-1/6*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","A",0
58,1,118,0,0.915768," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\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)}}}{6 \, d}"," ",0,"1/6*((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","A",0
59,1,164,0,1.133268," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\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}}}{6 \, d}"," ",0,"-1/6*(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","A",0
60,1,207,0,1.119473," ","integrate(cos(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\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}}}{6 \, d}"," ",0,"1/6*(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)/d","A",0
61,1,211,0,0.619063," ","integrate(sec(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\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}}}{60 \, d}"," ",0,"-1/60*(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)/d","A",0
62,1,165,0,0.394237," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\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}}}{20 \, d}"," ",0,"1/20*(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
63,1,119,0,0.747148," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\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}}}{60 \, d}"," ",0,"-1/60*((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
64,1,67,0,0.891576," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\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}}}{60 \, a^{3} d}"," ",0,"1/60*(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
65,1,47,0,0.724624," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\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}}}{20 \, a^{3} d}"," ",0,"1/20*(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
66,1,67,0,0.763484," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\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}}}{60 \, a^{3} d}"," ",0,"1/60*(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
67,1,92,0,0.963489," ","integrate(1/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\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}}}{60 \, d}"," ",0,"-1/60*((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
68,1,137,0,1.212013," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\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}}}{20 \, d}"," ",0,"1/20*(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
69,1,184,0,1.022554," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\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}}}{60 \, d}"," ",0,"-1/60*(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","A",0
70,1,231,0,1.076180," ","integrate(sec(d*x+c)^7/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\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}}}{280 \, d}"," ",0,"-1/280*(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)/d","A",0
71,1,186,0,1.009432," ","integrate(sec(d*x+c)^6/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\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}}}{840 \, d}"," ",0,"1/840*(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
72,1,139,0,0.784893," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\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}}}{168 \, d}"," ",0,"-1/168*((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
73,1,87,0,1.022481," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\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}}}{280 \, a^{4} d}"," ",0,"1/280*(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
74,1,87,0,1.032372," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\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}}}{840 \, a^{4} d}"," ",0,"1/840*(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
75,1,87,0,0.791540," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\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}}}{840 \, a^{4} d}"," ",0,"1/840*(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
76,1,87,0,0.636310," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\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}}}{280 \, a^{4} d}"," ",0,"1/280*(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
77,1,112,0,1.192868," ","integrate(1/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\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}}}{168 \, d}"," ",0,"-1/168*((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
78,1,158,0,0.801884," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{\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}}}{840 \, d}"," ",0,"1/840*(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
79,1,204,0,1.094153," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\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}}}{280 \, d}"," ",0,"-1/280*(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
80,1,206,0,0.762285," ","integrate(sec(d*x+c)^7/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{2016 \, \sin\left(d x + c\right)}{{\left(a^{5} - \frac{a^{5} \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{8127 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1512 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{72 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{5}} + \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{5}}}{1008 \, d}"," ",0,"1/1008*(2016*sin(d*x + c)/((a^5 - a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (8127*sin(d*x + c)/(cos(d*x + c) + 1) + 1512*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 72*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^5 + 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^5)/d","A",0
81,1,159,0,0.689881," ","integrate(sec(d*x+c)^6/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{\frac{9765 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2730 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1008 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{5}} + \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*((9765*sin(d*x + c)/(cos(d*x + c) + 1) + 2730*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1008*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^5 + 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^5)/d","A",0
82,1,107,0,0.705618," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{420 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{180 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{5040 \, a^{5} d}"," ",0,"1/5040*(315*sin(d*x + c)/(cos(d*x + c) + 1) + 420*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 180*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
83,1,87,0,0.598782," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{63 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{42 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{18 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{1008 \, a^{5} d}"," ",0,"1/1008*(63*sin(d*x + c)/(cos(d*x + c) + 1) + 42*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 18*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
84,1,67,0,0.596842," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{18 \, \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)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{720 \, a^{5} d}"," ",0,"1/720*(45*sin(d*x + c)/(cos(d*x + c) + 1) - 18*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
85,1,87,0,0.501643," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{63 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{42 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{18 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{1008 \, a^{5} d}"," ",0,"1/1008*(63*sin(d*x + c)/(cos(d*x + c) + 1) - 42*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 18*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
86,1,107,0,0.454818," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{420 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{180 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{5040 \, a^{5} d}"," ",0,"1/5040*(315*sin(d*x + c)/(cos(d*x + c) + 1) - 420*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 180*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
87,1,132,0,0.677323," ","integrate(1/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{\frac{9765 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2730 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1008 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{10080 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*((9765*sin(d*x + c)/(cos(d*x + c) + 1) - 2730*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1008*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 10080*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^5)/d","A",0
88,1,178,0,1.055669," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{2016 \, \sin\left(d x + c\right)}{{\left(a^{5} + \frac{a^{5} \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{8127 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1512 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{72 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{10080 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{5}}}{1008 \, d}"," ",0,"1/1008*(2016*sin(d*x + c)/((a^5 + a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (8127*sin(d*x + c)/(cos(d*x + c) + 1) - 1512*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 72*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 10080*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^5)/d","A",0
89,1,224,0,1.129798," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{5040 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{11 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{5} + \frac{2 \, a^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{110565 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15750 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3024 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{450 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{156240 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*(5040*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 11*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^5 + 2*a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (110565*sin(d*x + c)/(cos(d*x + c) + 1) - 15750*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3024*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 450*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 156240*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^5)/d","A",0
90,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{1}{2} \, {\left(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)}^{\frac{3}{4}} d \int \frac{{\left({\left(\cos\left(6 \, d x + 6 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + {\left(\cos\left(2 \, d x + 2 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left({\left(\cos\left(2 \, d x + 2 \, c\right) \sin\left(6 \, d x + 6 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(4 \, d x + 4 \, c\right) - \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(\cos\left(6 \, d x + 6 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + 2 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{2 \, {\left({\left(2 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right) \cos\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, \sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}\,{d x} + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} \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)}}{3 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} d}"," ",0,"4/3*(3*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*sqrt(a)*d*integrate((((cos(6*d*x + 6*c)*cos(2*d*x + 2*c) + 2*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + sin(6*d*x + 6*c)*sin(2*d*x + 2*c) + 2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + (cos(2*d*x + 2*c)*sin(6*d*x + 6*c) + 2*cos(2*d*x + 2*c)*sin(4*d*x + 4*c) - cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((cos(2*d*x + 2*c)*sin(6*d*x + 6*c) + 2*cos(2*d*x + 2*c)*sin(4*d*x + 4*c) - cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (cos(6*d*x + 6*c)*cos(2*d*x + 2*c) + 2*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + sin(6*d*x + 6*c)*sin(2*d*x + 2*c) + 2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))/(((2*(2*cos(4*d*x + 4*c) + cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 4*cos(4*d*x + 4*c)^2 + 4*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + 2*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 4*sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (2*(2*cos(4*d*x + 4*c) + cos(2*d*x + 2*c))*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 4*cos(4*d*x + 4*c)^2 + 4*cos(4*d*x + 4*c)*cos(2*d*x + 2*c) + cos(2*d*x + 2*c)^2 + 2*(2*sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 4*sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + sin(2*d*x + 2*c)^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)), x) + sqrt(a)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*d)","F",0
93,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
94,1,146,0,1.328898," ","integrate((a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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,"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
95,1,791,0,1.575047," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{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)}}{4 \, d}"," ",0,"1/4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
96,1,1059,0,1.179447," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{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)}}{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)))/d","B",0
97,1,1921,0,2.075177," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{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)}}{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)))/d","B",0
98,1,6638,0,2.827186," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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}}{768 \, {\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)} d}"," ",0,"-1/768*(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))/((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
99,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
103,1,997,0,1.001618," ","integrate((a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\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}}{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))/((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
104,1,803,0,1.194438," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{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}}{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))/d","B",0
105,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
111,1,1395,0,0.918057," ","integrate((a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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}}{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))/((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
112,1,1383,0,1.011733," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/4*(18*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((4*a^2*sin(3*d*x + 3*c) + 5*a^2*sin(2*d*x + 2*c) + 4*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*cos(2*d*x + 2*c)^2*sin(d*x + c) + a^2*sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*a^2*cos(2*d*x + 2*c)*sin(d*x + c) + a^2*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (4*a^2*cos(3*d*x + 3*c) + 5*a^2*cos(2*d*x + 2*c) + 4*a^2*cos(d*x + c) + 5*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c)^2 + a^2*cos(d*x + c) + (a^2*cos(d*x + c) - a^2)*sin(2*d*x + 2*c)^2 - a^2 + 2*(a^2*cos(d*x + c) - a^2)*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 5*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))/((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
113,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(-a*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
117,1,146,0,1.680635," ","integrate((a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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,"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
118,1,791,0,1.279150," ","integrate(cos(d*x+c)*(a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}}{4 \, d}"," ",0,"-1/4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
119,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
120,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
121,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
122,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
123,-2,0,0,0.000000," ","integrate(1/(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
124,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
125,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
126,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(a*sec(d*x + c) + a)^(3/2), x)","F",0
127,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(a*sec(d*x + c) + a)^(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
129,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
130,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(-3/2), x)","F",0
132,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
133,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
134,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(5/2), x)","F",0
137,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
138,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
139,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(-5/2), x)","F",0
140,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
141,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a-a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{-a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(-a*sec(d*x + c) + a), x)","F",0
142,-2,0,0,0.000000," ","integrate(1/(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
143,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^3, x)","F",0
144,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^2, x)","F",0
145,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c), x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3), x)","F",0
147,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*cos(d*x + c), x)","F",0
148,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^3, x)","F",0
149,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^2, x)","F",0
150,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*sec(d*x + c), x)","F",0
151,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3), x)","F",0
152,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/3)*cos(d*x + c), x)","F",0
153,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(a*sec(d*x + c) + a)^(1/3), x)","F",0
154,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(1/3), x)","F",0
155,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(1/3), x)","F",0
156,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
157,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(-1/3), x)","F",0
158,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
159,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(5/3), x)","F",0
161,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(5/3), x)","F",0
162,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
163,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(-5/3), x)","F",0
164,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(a*sec(d*x + c) + a)^(5/3), x)","F",0
165,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
166,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
167,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
168,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
169,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
170,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
172,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
173,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
174,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
175,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
176,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
177,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
178,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sec(d*x + c)^(7/2), x)","F",0
179,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
181,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
182,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(5/2), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(7/2), x)","F",0
185,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sec(d*x + c)^(9/2), x)","F",0
186,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
188,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
189,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(3/2), x)","F",0
190,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(5/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(7/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^4/sec(d*x + c)^(9/2), x)","F",0
193,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
195,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
196,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
197,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
198,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
199,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
200,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
201,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
206,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
207,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
208,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
209,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate(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
213,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
215,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
216,-2,0,0,0.000000," ","integrate(1/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
217,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
218,1,1264,0,1.061621," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{16 \, {\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)} d}"," ",0,"-1/16*(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))))*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
219,1,662,0,0.704618," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(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))))*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
220,1,241,0,0.650907," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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*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
221,1,20,0,0.622332," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sin(1/2*d*x + 1/2*c)/d","A",0
222,1,113,0,0.583216," ","integrate((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)} \sqrt{a}}{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))))*sqrt(a)/d","A",0
223,1,203,0,0.670132," ","integrate((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)} \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))))*sqrt(a)/d","B",0
224,1,293,0,0.755290," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\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)} \sqrt{a}}{280 \, d}"," ",0,"1/280*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))))*sqrt(a)/d","B",0
225,1,2361,0,0.907039," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{96 \, {\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)} d}"," ",0,"-1/96*(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))))*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
226,1,2244,0,0.880012," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{16 \, {\left(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\right)} d}"," ",0,"-1/16*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*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
227,1,1143,0,0.680739," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\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)} \sqrt{a}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/4*(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))*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
228,1,274,0,0.872681," ","integrate((a+a*sec(d*x+c))^(3/2)/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)} \sqrt{a}}{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))*sqrt(a)/d","B",0
229,1,38,0,0.565608," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{3 \, d}"," ",0,"1/3*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*sqrt(a)/d","A",0
230,1,210,0,0.870246," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{20 \, d}"," ",0,"1/20*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sqrt(a)/d","B",0
231,1,303,0,0.614237," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(735 \, a \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 175 \, a \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 735 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 175 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 63 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 30 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, a \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 175 \, a \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 735 \, a \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} \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))))*sqrt(a)/d","B",0
232,1,396,0,1.104796," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3780 \, a \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1050 \, a \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 378 \, a \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 3780 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 1050 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 378 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 135 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, a \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 378 \, a \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1050 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 3780 \, a \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} \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))))*sqrt(a)/d","B",0
233,1,3860,0,1.578352," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{768 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/768*(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))))*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
234,1,3469,0,0.989556," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\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)} \sqrt{a}}{96 \, {\left(\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\right)} d}"," ",0,"1/96*(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))))*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
235,1,2826,0,5.134777," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{{\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)} \sqrt{a}}{16 \, {\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)} d}"," ",0,"-1/16*(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))*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
236,-1,0,0,0.000000," ","integrate((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
237,1,593,0,0.656196," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),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)} \sqrt{a}}{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))))*sqrt(a)/d","B",0
238,1,60,0,0.588345," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),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)} \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))*sqrt(a)/d","A",0
239,1,323,0,0.750981," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{168 \, d}"," ",0,"1/168*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*sqrt(a)/d","B",0
240,1,422,0,0.719976," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(8190 \, a^{2} \cos\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2100 \, a^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 756 \, a^{2} \cos\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \cos\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 8190 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{8}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 2100 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 756 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{4}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 225 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) \sin\left(\frac{2}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 70 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, a^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 756 \, a^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 2100 \, a^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 8190 \, a^{2} \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)} \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))))*sqrt(a)/d","B",0
241,1,521,0,0.761476," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(31878 \, a^{2} \cos\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 8778 \, a^{2} \cos\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 3465 \, a^{2} \cos\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1287 \, a^{2} \cos\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \cos\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 31878 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{10}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 8778 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{8}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 3465 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{6}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1287 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{4}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 385 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) \sin\left(\frac{2}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 126 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, a^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1287 \, a^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 3465 \, a^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 8778 \, a^{2} \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 31878 \, a^{2} \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{22176 \, d}"," ",0,"1/22176*sqrt(2)*(31878*a^2*cos(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 8778*a^2*cos(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 3465*a^2*cos(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 1287*a^2*cos(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) + 385*a^2*cos(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c)))*sin(11/2*d*x + 11/2*c) - 31878*a^2*cos(11/2*d*x + 11/2*c)*sin(10/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 8778*a^2*cos(11/2*d*x + 11/2*c)*sin(8/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 3465*a^2*cos(11/2*d*x + 11/2*c)*sin(6/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1287*a^2*cos(11/2*d*x + 11/2*c)*sin(4/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 385*a^2*cos(11/2*d*x + 11/2*c)*sin(2/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 126*a^2*sin(11/2*d*x + 11/2*c) + 385*a^2*sin(9/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1287*a^2*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 3465*a^2*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 8778*a^2*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 31878*a^2*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))*sqrt(a)/d","B",0
242,1,121,0,0.594179," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/4),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{4}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{4}} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4*(sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/4)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(1/4))","B",0
243,1,241,0,0.619764," ","integrate(sec(f*x+e)^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2\right)\right)}}{2 \, f}"," ",0,"1/2*sqrt(a)*(log(2*cos(1/2*f*x + 1/2*e)^2 + 2*sin(1/2*f*x + 1/2*e)^2 + 2*sqrt(2)*cos(1/2*f*x + 1/2*e) + 2*sqrt(2)*sin(1/2*f*x + 1/2*e) + 2) - log(2*cos(1/2*f*x + 1/2*e)^2 + 2*sin(1/2*f*x + 1/2*e)^2 + 2*sqrt(2)*cos(1/2*f*x + 1/2*e) - 2*sqrt(2)*sin(1/2*f*x + 1/2*e) + 2) + log(2*cos(1/2*f*x + 1/2*e)^2 + 2*sin(1/2*f*x + 1/2*e)^2 - 2*sqrt(2)*cos(1/2*f*x + 1/2*e) + 2*sqrt(2)*sin(1/2*f*x + 1/2*e) + 2) - log(2*cos(1/2*f*x + 1/2*e)^2 + 2*sin(1/2*f*x + 1/2*e)^2 - 2*sqrt(2)*cos(1/2*f*x + 1/2*e) - 2*sqrt(2)*sin(1/2*f*x + 1/2*e) + 2))/f","B",0
244,1,353,0,0.987631," ","integrate((-sec(f*x+e))^(1/2)*(a-a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a} {\left(\log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) + 2\right) + \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) + 2\right) - \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right)\right)\right) + 2\right)\right)}}{2 \, f}"," ",0,"-1/2*sqrt(a)*(log(2*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 + 2*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e))) + 2*sqrt(2)*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e))) + 2) + log(2*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 + 2*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e))) - 2*sqrt(2)*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e))) + 2) - log(2*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 + 2*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e))) + 2*sqrt(2)*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e))) + 2) - log(2*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 + 2*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(f*x + e), cos(f*x + e))) - 2*sqrt(2)*sin(1/2*arctan2(sin(f*x + e), cos(f*x + e))) + 2))/f","B",0
245,1,876,0,0.689561," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a} d}"," ",0,"-1/4*(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))))/((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
246,1,476,0,0.820018," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)}{2 \, \sqrt{a} d}"," ",0,"-1/2*(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))/(sqrt(a)*d)","B",0
247,1,90,0,0.671763," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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)}{2 \, \sqrt{a} 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))/(sqrt(a)*d)","A",0
248,1,104,0,0.593759," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)}{2 \, \sqrt{a} 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))/(sqrt(a)*d)","A",0
249,1,282,0,0.663867," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}{6 \, \sqrt{a} 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))))/(sqrt(a)*d)","B",0
250,1,357,0,0.840026," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\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)}}{60 \, \sqrt{a} 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))))/(sqrt(a)*d)","B",0
251,1,4934,0,1.026233," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{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)}{4 \, {\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} d}"," ",0,"-1/4*(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))))/((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
252,1,2122,0,1.486043," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{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)}{4 \, {\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} 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))))/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 4*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*sqrt(a)*d)","B",0
253,-1,0,0,0.000000," ","integrate(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
254,1,1031,0,1.504933," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{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)}{4 \, {\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} 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))/((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
255,1,7176,0,1.004557," ","integrate(1/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{4 \, {\left(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)\right)} 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))*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))*d)","B",0
256,-1,0,0,0.000000," ","integrate(1/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
257,-2,0,0,0.000000," ","integrate(1/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
258,1,9048,0,6.100069," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{140 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \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{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(75 \, \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) + 24 \, \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) - 24 \, \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) - 75 \, \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) - 35 \, \sin\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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 300 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 96 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 32 \, {\left(24 \, \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) + 75 \, \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) + 35 \, \sin\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) - 96 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) - 300 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) - 140 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) - 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) + 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) - 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) - 115 \, {\left(2 \, {\left(7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\left(7 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 49 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \cos\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\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} + 49 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \sin\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, \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) + 115 \, {\left(2 \, {\left(7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\left(7 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 49 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \cos\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\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} + 49 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \sin\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, \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) - 140 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \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{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(75 \, \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) + 24 \, \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) - 24 \, \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) - 75 \, \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) - 35 \, \cos\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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 300 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 96 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) - 32 \, {\left(24 \, \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) + 75 \, \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) + 35 \, \cos\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) + 96 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 300 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) - 560 \, \cos\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) + 140 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 560 \, \cos\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)}{32 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \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(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \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} + 14 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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} d}"," ",0,"-1/32*(140*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 4*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*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(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(75*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 24*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 24*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 35*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 300*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 96*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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))) + 32*(24*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 75*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 35*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))) - 96*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) - 300*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) - 140*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) - 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) + 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) - 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) - 115*(2*(7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 14*(7*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 49*cos(4*d*x + 4*c)^2 + 49*cos(2*d*x + 2*c)^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) + 64*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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 + 14*(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 + 49*sin(4*d*x + 4*c)^2 + 98*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sin(2*d*x + 2*c)^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) + 64*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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 + 14*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) + 115*(2*(7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 14*(7*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 49*cos(4*d*x + 4*c)^2 + 49*cos(2*d*x + 2*c)^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) + 64*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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 + 14*(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 + 49*sin(4*d*x + 4*c)^2 + 98*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sin(2*d*x + 2*c)^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) + 64*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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 + 14*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) - 140*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 4*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*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(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(75*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 24*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 24*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 35*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 300*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 96*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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))) - 32*(24*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 75*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 35*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))) + 96*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) + 300*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) - 560*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))) + 140*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 560*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))))/((sqrt(2)*a^2*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*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(6*d*x + 6*c)^2 + 49*sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*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 + 14*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2 + 2*(7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(6*d*x + 6*c) + 14*(7*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(6*d*x + 6*c) + 7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*sqrt(2)*a^2*cos(2*d*x + 2*c) + 8*sqrt(2)*a^2*cos(3/2*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))) + sqrt(2)*a^2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*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(6*d*x + 6*c) + 7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*a^2*sin(4*d*x + 4*c) + sqrt(2)*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 7*sqrt(2)*a^2*sin(4*d*x + 4*c) + 7*sqrt(2)*a^2*sin(2*d*x + 2*c) + 8*sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(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(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 7*sqrt(2)*a^2*sin(4*d*x + 4*c) + 7*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(6*d*x + 6*c) + 7*sqrt(2)*a^2*sin(4*d*x + 4*c) + 7*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
259,1,4988,0,2.560389," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(19 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(19 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 176 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 176 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{32 \, {\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} d}"," ",0,"1/32*(44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(19*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(19*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 176*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 176*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((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
260,-1,0,0,0.000000," ","integrate(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
261,1,2875,0,1.468642," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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)}{32 \, {\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} 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))/((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
262,1,3049,0,1.058592," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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)}{32 \, {\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} 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))/((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)*d)","B",0
263,-1,0,0,0.000000," ","integrate(1/(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
264,-1,0,0,0.000000," ","integrate(1/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
265,1,1643,0,1.083357," ","integrate(sec(d*x+c)^(7/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{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)}{16 \, {\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)} d}"," ",0,"1/16*(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))))/((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
266,1,873,0,1.245995," ","integrate(sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(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))))/((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
267,1,473,0,0.929817," ","integrate(sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)}{2 \, d}"," ",0,"-1/2*(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))/d","B",0
268,1,87,0,1.289936," ","integrate(sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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)}{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))/d","B",0
269,1,101,0,1.090867," ","integrate(1/sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)}{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))/d","A",0
270,1,279,0,0.915146," ","integrate(1/sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}{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))))/d","B",0
271,1,354,0,0.758857," ","integrate(1/sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\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)}}{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))))/d","B",0
272,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(4/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(4/3), x)","F",0
273,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(1/3), x)","F",0
274,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/(e*sec(d*x + c))^(2/3), x)","F",0
275,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(8/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{8}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(8/3), x)","F",0
276,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(5/3), x)","F",0
277,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3), x)","F",0
278,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/(e*sec(d*x + c))^(1/3), x)","F",0
279,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sec\left(d x + c\right) + a}}{\left(e \sec\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)/(e*sec(d*x + c))^(4/3), x)","F",0
280,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(2/3)/sqrt(a*sec(d*x + c) + a), x)","F",0
281,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(1/3)/sqrt(a*sec(d*x + c) + a), x)","F",0
282,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(1/3)), x)","F",0
283,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3)), x)","F",0
284,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^(4/3), x)","F",0
285,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^(4/3), x)","F",0
286,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^(5/3), x)","F",0
287,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)/sec(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}{\sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(4/3)/sec(d*x + c)^(1/3), x)","F",0
288,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^4,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{4} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^4*sec(f*x + e)^n, x)","F",0
289,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{3} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*sec(f*x + e)^n, x)","F",0
290,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{2} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*sec(f*x + e)^n, x)","F",0
291,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
292,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{n}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(a*sec(f*x + e) + a), x)","F",0
293,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(a*sec(f*x + e) + a)^2, x)","F",0
294,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \sec\left(f x + e\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n*(sec(f*x + e) + 1)^(5/2), x)","F",0
295,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \sec\left(f x + e\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
296,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sec\left(f x + e\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate(sec(f*x + e)^n*sqrt(sec(f*x + e) + 1), x)","F",0
297,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(1+sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/sqrt(sec(f*x + e) + 1), x)","F",0
298,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(1+sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{n}}{{\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(sec(f*x + e) + 1)^(3/2), x)","F",0
299,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(-\sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
300,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(-\sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*sqrt(sec(f*x + e) + 1), x)","F",0
301,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/sqrt(sec(f*x + e) + 1), x)","F",0
302,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{{\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/(sec(f*x + e) + 1)^(3/2), x)","F",0
303,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
304,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*sqrt(sec(f*x + e) + 1), x)","F",0
305,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/sqrt(sec(f*x + e) + 1), x)","F",0
306,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(sec(f*x + e) + 1)^(3/2), x)","F",0
307,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(5/2)*sec(f*x + e)^n, x)","F",0
308,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*sec(f*x + e)^n, x)","F",0
309,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
310,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/sqrt(a*sec(f*x + e) + a), x)","F",0
311,0,0,0,0.000000," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(f x + e\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(f*x + e)^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
312,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*(-sec(f*x + e))^n, x)","F",0
313,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
314,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/sqrt(a*sec(f*x + e) + a), x)","F",0
315,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
316,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
317,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
318,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/sqrt(a*sec(f*x + e) + a), x)","F",0
319,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(a*sec(f*x + e) + a)^(3/2), x)","F",0
320,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{5}{2}} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(5/2)*(-sec(f*x + e))^n, x)","F",0
321,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(3/2)*(-sec(f*x + e))^n, x)","F",0
322,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
323,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{-a \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/sqrt(-a*sec(f*x + e) + a), x)","F",0
324,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(-\sec\left(f x + e\right)\right)^{n}}{{\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n/(-a*sec(f*x + e) + a)^(3/2), x)","F",0
325,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(3/2)*sec(f*x + e)^n, x)","F",0
326,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
327,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
328,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
329,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sec\left(f x + e\right) + 1\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((sec(f*x + e) + 1)^m*sec(f*x + e)^n, x)","F",0
330,0,0,0,0.000000," ","integrate((1-sec(f*x+e))^m*sec(f*x+e)^n,x, algorithm=""maxima"")","\int {\left(-\sec\left(f x + e\right) + 1\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((-sec(f*x + e) + 1)^m*sec(f*x + e)^n, x)","F",0
331,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
332,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
333,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(-\sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*(sec(f*x + e) + 1)^m, x)","F",0
334,0,0,0,0.000000," ","integrate((1-sec(f*x+e))^m*(-sec(f*x+e))^n,x, algorithm=""maxima"")","\int \left(-\sec\left(f x + e\right)\right)^{n} {\left(-\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-sec(f*x + e))^n*(-sec(f*x + e) + 1)^m, x)","F",0
335,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(-sec(f*x + e))^n, x)","F",0
336,0,0,0,0.000000," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{m} \left(-\sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^m*(-sec(f*x + e))^n, x)","F",0
337,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*(sec(f*x + e) + 1)^m, x)","F",0
338,0,0,0,0.000000," ","integrate((1-sec(f*x+e))^m*(d*sec(f*x+e))^n,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{n} {\left(-\sec\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n*(-sec(f*x + e) + 1)^m, x)","F",0
339,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
340,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(-a \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
341,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^4, x)","F",0
342,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
343,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
344,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
345,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m, x)","F",0
346,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m*cos(f*x + e), x)","F",0
347,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(a*sec(f*x + e) + a)^m, x)","F",0
348,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(a*sec(f*x + e) + a)^m, x)","F",0
349,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m/sqrt(d*sec(f*x + e)), x)","F",0
350,0,0,0,0.000000," ","integrate((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(f x + e\right) + a\right)}^{m}}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^m/(d*sec(f*x + e))^(3/2), x)","F",0
351,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*cos(d*x + c)^(7/2), x)","F",0
352,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
353,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
355,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
356,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
358,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
359,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
360,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(7/2), x)","F",0
361,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
362,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
364,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
365,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
366,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
367,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(9/2), x)","F",0
368,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
369,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
370,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
371,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
372,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
373,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
375,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
376,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
377,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
378,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
379,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
380,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
381,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
382,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^2, x)","F",0
383,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
384,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
385,-1,0,0,0.000000," ","integrate(1/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
386,-1,0,0,0.000000," ","integrate(1/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
387,-1,0,0,0.000000," ","integrate(1/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
388,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a)^3, x)","F",0
390,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a)^3, x)","F",0
391,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a)^3, x)","F",0
392,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(1/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
394,-1,0,0,0.000000," ","integrate(1/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
395,-1,0,0,0.000000," ","integrate(1/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
396,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,1,293,0,0.865601," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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)} \sqrt{a}}{280 \, d}"," ",0,"1/280*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))))*sqrt(a)/d","B",0
399,1,203,0,0.966174," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(30 \, \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 30 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 6 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} \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))))*sqrt(a)/d","B",0
400,1,113,0,1.233860," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{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))))*sqrt(a)/d","A",0
401,1,20,0,0.589121," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sin(1/2*d*x + 1/2*c)/d","A",0
402,1,241,0,1.549115," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\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*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
403,1,662,0,1.504357," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(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))))*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
404,1,1264,0,0.721115," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{16 \, {\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)} d}"," ",0,"-1/16*(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))))*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
405,1,303,0,0.563576," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2),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)} \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))))*sqrt(a)/d","B",0
406,1,210,0,1.564215," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(20 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 5 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 2 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 20 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{20 \, d}"," ",0,"1/20*sqrt(2)*(20*a*cos(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) + 5*a*cos(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c)))*sin(5/2*d*x + 5/2*c) - 20*a*cos(5/2*d*x + 5/2*c)*sin(4/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 5*a*cos(5/2*d*x + 5/2*c)*sin(2/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 2*a*sin(5/2*d*x + 5/2*c) + 5*a*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 20*a*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sqrt(a)/d","B",0
407,1,38,0,1.577928," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{3 \, d}"," ",0,"1/3*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*sqrt(a)/d","A",0
408,1,274,0,1.293506," ","integrate((a+a*sec(d*x+c))^(3/2)*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)} \sqrt{a}}{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))*sqrt(a)/d","B",0
409,1,1143,0,1.792321," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\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)} \sqrt{a}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/4*(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))*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
410,1,2244,0,1.435249," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{16 \, {\left(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\right)} d}"," ",0,"-1/16*(56*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 24*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 12*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 28*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 4*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*(3*sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 7*(a*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 4*a*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*(2*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*cos(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 4*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + a)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 4*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + 7*sqrt(2)*a*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 3*sqrt(2)*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(8/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 28*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 12*(2*sqrt(2)*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sqrt(2)*a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) - 7*sqrt(2)*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*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
411,1,2361,0,1.401591," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{96 \, {\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)} d}"," ",0,"-1/96*(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))))*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
412,1,422,0,1.300445," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2),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)} \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))))*sqrt(a)/d","B",0
413,1,323,0,0.918239," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(315 \, a^{2} \cos\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \cos\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \cos\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 315 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{6}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 77 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{4}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(\frac{2}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 6 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 77 \, a^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 315 \, a^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{168 \, d}"," ",0,"1/168*sqrt(2)*(315*a^2*cos(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 77*a^2*cos(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) + 21*a^2*cos(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c)))*sin(7/2*d*x + 7/2*c) - 315*a^2*cos(7/2*d*x + 7/2*c)*sin(6/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 77*a^2*cos(7/2*d*x + 7/2*c)*sin(4/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*a^2*cos(7/2*d*x + 7/2*c)*sin(2/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 6*a^2*sin(7/2*d*x + 7/2*c) + 21*a^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 77*a^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 315*a^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*sqrt(a)/d","B",0
414,1,60,0,1.263185," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),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)} \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))*sqrt(a)/d","A",0
415,1,593,0,1.452063," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),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)} \sqrt{a}}{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))))*sqrt(a)/d","B",0
416,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,1,2826,0,10.408476," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{{\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)} \sqrt{a}}{16 \, {\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)} d}"," ",0,"-1/16*(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))*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
418,1,3469,0,0.952348," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\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)} \sqrt{a}}{96 \, {\left(\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\right)} d}"," ",0,"1/96*(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))))*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
419,1,3860,0,1.661149," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{768 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/768*(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))))*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
420,1,357,0,1.535572," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\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)}}{60 \, \sqrt{a} 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))))/(sqrt(a)*d)","B",0
421,1,282,0,1.478103," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}{6 \, \sqrt{a} 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))))/(sqrt(a)*d)","B",0
422,1,104,0,1.265636," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)}{2 \, \sqrt{a} 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))/(sqrt(a)*d)","A",0
423,1,90,0,1.282443," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\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)}{2 \, \sqrt{a} 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))/(sqrt(a)*d)","A",0
424,1,476,0,0.747522," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\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)}{2 \, \sqrt{a} d}"," ",0,"-1/2*(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))/(sqrt(a)*d)","B",0
425,1,876,0,2.799826," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{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)}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{a} d}"," ",0,"-1/4*(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))))/((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
426,1,1646,0,1.903817," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{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)}{16 \, {\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} d}"," ",0,"1/16*(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))))/((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
427,-2,0,0,0.000000," ","integrate(cos(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
428,-1,0,0,0.000000," ","integrate(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
429,1,7176,0,0.724569," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\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)} \sqrt{a}}{4 \, {\left(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)\right)} 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))*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))*d)","B",0
430,1,1031,0,0.599773," ","integrate(1/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{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)}{4 \, {\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} 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))/((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
431,-1,0,0,0.000000," ","integrate(1/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
432,1,2122,0,0.692700," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{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)}{4 \, {\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} 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))))/((sqrt(2)*a*cos(2*d*x + 2*c)^2 + 4*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*a*sin(2*d*x + 2*c)^2 + 4*sqrt(2)*a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*a*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*a*cos(2*d*x + 2*c) + 4*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2)*a)*sqrt(a)*d)","B",0
433,1,4934,0,1.687729," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{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)}{4 \, {\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} d}"," ",0,"-1/4*(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))))/((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
434,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate(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
436,1,3049,0,1.826889," ","integrate(1/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{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)}{32 \, {\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} 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))/((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)*d)","B",0
437,1,2875,0,2.501201," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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)}{32 \, {\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} 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))/((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
438,-1,0,0,0.000000," ","integrate(1/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
439,1,4988,0,1.003313," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(19 \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 44 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 6 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 12 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 43 \, {\left(2 \, {\left(6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 36 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 8 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 6 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(19 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 19 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 11 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 76 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 176 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 44 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 176 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)}{32 \, {\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} d}"," ",0,"1/32*(44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(19*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 44*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*(sqrt(2)*cos(4*d*x + 4*c)^2 + 36*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(4*d*x + 4*c)^2 + 12*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(4*d*x + 4*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(4*d*x + 4*c) + 6*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 12*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 43*(2*(6*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 36*cos(2*d*x + 2*c)^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(4*d*x + 4*c)^2 + 12*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 36*sin(2*d*x + 2*c)^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c) + 4*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(4*d*x + 4*c) + 6*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 12*cos(2*d*x + 2*c) + 1)*log(cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(19*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 19*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 11*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 76*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 4*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 176*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 44*(cos(4*d*x + 4*c) + 6*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 176*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))/((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
440,1,9048,0,3.569937," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{140 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \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{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, {\left(75 \, \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) + 24 \, \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) - 24 \, \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) - 75 \, \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) - 35 \, \sin\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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 300 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 96 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 32 \, {\left(24 \, \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) + 75 \, \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) + 35 \, \sin\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) - 96 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) - 300 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) - 140 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) - 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) + 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) - 40 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, {\left(\sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, \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) - 115 \, {\left(2 \, {\left(7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\left(7 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 49 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \cos\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\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} + 49 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \sin\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, \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) + 115 \, {\left(2 \, {\left(7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\left(7 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 49 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \cos\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, {\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} + 49 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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)} \sin\left(\frac{5}{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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 16 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 64 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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} + 14 \, \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) - 140 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 4 \, \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 8 \, \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{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(75 \, \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) + 24 \, \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) - 24 \, \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) - 75 \, \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) - 35 \, \cos\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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 300 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 96 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) - 32 \, {\left(24 \, \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) + 75 \, \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) + 35 \, \cos\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) + 96 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 300 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) - 560 \, \cos\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) + 140 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 7 \, \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 560 \, \cos\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)}{32 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 49 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \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(6 \, d x + 6 \, c\right)^{2} + 49 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 98 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 49 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 16 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 64 \, \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} + 14 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} + 2 \, {\left(7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 14 \, {\left(7 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} a^{2} \cos\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, \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) + 14 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, \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) + 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{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, {\left(\sqrt{2} a^{2} \sin\left(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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(6 \, d x + 6 \, c\right) + 7 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, \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} d}"," ",0,"-1/32*(140*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 4*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*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(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*(75*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 24*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 24*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 35*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 300*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 96*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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))) + 32*(24*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 75*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 35*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))) - 96*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) - 300*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) - 140*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c))*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) - 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) + 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) - 40*(sqrt(2)*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 49*sqrt(2)*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*(7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 14*(7*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*cos(6*d*x + 6*c) + 7*sqrt(2)*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 8*sqrt(2)*sin(3/2*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*(sqrt(2)*sin(6*d*x + 6*c) + 7*sqrt(2)*sin(4*d*x + 4*c) + 7*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 14*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) - 115*(2*(7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 14*(7*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 49*cos(4*d*x + 4*c)^2 + 49*cos(2*d*x + 2*c)^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) + 64*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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 + 14*(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 + 49*sin(4*d*x + 4*c)^2 + 98*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sin(2*d*x + 2*c)^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) + 64*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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 + 14*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) + 115*(2*(7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 14*(7*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 49*cos(4*d*x + 4*c)^2 + 49*cos(2*d*x + 2*c)^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) + 64*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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 + 14*(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 + 49*sin(4*d*x + 4*c)^2 + 98*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sin(2*d*x + 2*c)^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*sin(2*d*x + 2*c) + 8*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))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 16*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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))) + 64*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 8*(sin(6*d*x + 6*c) + 7*sin(4*d*x + 4*c) + 7*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 + 14*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) - 140*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 4*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 8*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(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(75*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 24*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 24*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 75*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 35*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 300*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 96*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 8*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))) - 32*(24*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 75*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 35*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))) + 96*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) + 300*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*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))) - 560*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))) + 140*(cos(6*d*x + 6*c) + 7*cos(4*d*x + 4*c) + 7*cos(2*d*x + 2*c) + 1)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 560*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))))/((sqrt(2)*a^2*cos(6*d*x + 6*c)^2 + 49*sqrt(2)*a^2*cos(4*d*x + 4*c)^2 + 49*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*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(6*d*x + 6*c)^2 + 49*sqrt(2)*a^2*sin(4*d*x + 4*c)^2 + 98*sqrt(2)*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 49*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 16*sqrt(2)*a^2*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 64*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 + 14*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2 + 2*(7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(6*d*x + 6*c) + 14*(7*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(6*d*x + 6*c) + 7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*sqrt(2)*a^2*cos(2*d*x + 2*c) + 8*sqrt(2)*a^2*cos(3/2*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))) + sqrt(2)*a^2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*a^2*cos(6*d*x + 6*c) + 7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*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(6*d*x + 6*c) + 7*sqrt(2)*a^2*cos(4*d*x + 4*c) + 7*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))) + 14*(sqrt(2)*a^2*sin(4*d*x + 4*c) + sqrt(2)*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 7*sqrt(2)*a^2*sin(4*d*x + 4*c) + 7*sqrt(2)*a^2*sin(2*d*x + 2*c) + 8*sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(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(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*(sqrt(2)*a^2*sin(6*d*x + 6*c) + 7*sqrt(2)*a^2*sin(4*d*x + 4*c) + 7*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(6*d*x + 6*c) + 7*sqrt(2)*a^2*sin(4*d*x + 4*c) + 7*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
441,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{3} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^3*(d*cos(f*x + e))^n, x)","F",0
442,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)}^{2} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)^2*(d*cos(f*x + e))^n, x)","F",0
443,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(a \sec\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sec(f*x + e) + a)*(d*cos(f*x + e))^n, x)","F",0
444,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+a*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{a \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(a*sec(f*x + e) + a), x)","F",0
445,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+a*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{{\left(a \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(a*sec(f*x + e) + a)^2, x)","F",0
446,1,95,0,0.325711," ","integrate(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 - 3 \, b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a - 3*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
447,1,70,0,0.411246," ","integrate(sec(d*x+c)^3*(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 - 3 \, 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 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*b - 3*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
448,1,58,0,0.331711," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{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 \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(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*tan(d*x + c))/d","A",0
449,1,29,0,0.544733," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + b \tan\left(d x + c\right)}{d}"," ",0,"(a*log(sec(d*x + c) + tan(d*x + c)) + b*tan(d*x + c))/d","A",0
450,1,23,0,0.515560," ","integrate(a+b*sec(d*x+c),x, algorithm=""maxima"")","a x + \frac{b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d}"," ",0,"a*x + b*log(sec(d*x + c) + tan(d*x + c))/d","A",0
451,1,20,0,0.378780," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} b + a \sin\left(d x + c\right)}{d}"," ",0,"((d*x + c)*b + a*sin(d*x + c))/d","A",0
452,1,34,0,0.321475," ","integrate(cos(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 + 4 \, b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a + 4*b*sin(d*x + c))/d","A",0
453,1,46,0,0.323407," ","integrate(cos(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 - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*b)/d","A",0
454,1,57,0,0.331529," ","integrate(cos(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 - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} 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 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*b)/d","A",0
455,1,69,0,0.336313," ","integrate(cos(d*x+c)^5*(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 + 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}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b)/d","A",0
456,1,132,0,0.338635," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} + 8 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} b^{2} - 15 \, 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)}}{120 \, d}"," ",0,"1/120*(40*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 + 8*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*b^2 - 15*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)))/d","A",0
457,1,144,0,0.372723," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b - 3 \, 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 \, 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 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b - 3*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*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
458,1,84,0,0.340442," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} b^{2} - 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)} + 6 \, a^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*tan(d*x + c))*b^2 - 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)) + 6*a^2*tan(d*x + c))/d","A",0
459,1,80,0,0.347725," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{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 \, a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 8 \, a b \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(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*a^2*log(sec(d*x + c) + tan(d*x + c)) - 8*a*b*tan(d*x + c))/d","A",0
460,1,40,0,0.334037," ","integrate((a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{2 \, a b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{b^{2} \tan\left(d x + c\right)}{d}"," ",0,"a^2*x + 2*a*b*log(sec(d*x + c) + tan(d*x + c))/d + b^2*tan(d*x + c)/d","A",0
461,1,51,0,0.394115," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} a b + b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b + b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a^2*sin(d*x + c))/d","A",0
462,1,47,0,0.469047," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} + 4 \, {\left(d x + c\right)} b^{2} + 8 \, 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^2 + 4*(d*x + c)*b^2 + 8*a*b*sin(d*x + c))/d","A",0
463,1,60,0,0.344069," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b - 6 \, b^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b - 6*b^2*sin(d*x + c))/d","A",0
464,1,82,0,0.334877," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 64 \, {\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^{2}}{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^2 - 64*(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^2)/d","A",0
465,1,94,0,0.338662," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b^{2}}{240 \, d}"," ",0,"1/240*(16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*b^2)/d","A",0
466,1,181,0,0.465976," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} 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^{3} - 45 \, 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^{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 \, d}"," ",0,"1/240*(240*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2*b + 16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*b^3 - 45*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^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
467,1,158,0,0.353276," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{2} - b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, 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)} + 16 \, a^{3} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^2 - b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*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)) + 16*a^3*tan(d*x + c))/d","A",0
468,1,106,0,0.344044," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} b^{3} - 9 \, 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^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 36 \, a^{2} b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*b^3 - 9*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^3*log(sec(d*x + c) + tan(d*x + c)) + 36*a^2*b*tan(d*x + c))/d","A",0
469,1,93,0,0.356016," ","integrate((a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x - \frac{b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{4 \, d} + \frac{3 \, a^{2} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{3 \, a b^{2} \tan\left(d x + c\right)}{d}"," ",0,"a^3*x - 1/4*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))/d + 3*a^2*b*log(sec(d*x + c) + tan(d*x + c))/d + 3*a*b^2*tan(d*x + c)/d","A",0
470,1,66,0,0.373189," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a^{2} b + 3 \, 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^{3} \sin\left(d x + c\right) + 2 \, b^{3} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(6*(d*x + c)*a^2*b + 3*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a^3*sin(d*x + c) + 2*b^3*tan(d*x + c))/d","A",0
471,1,76,0,0.380910," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 12 \, {\left(d x + c\right)} a b^{2} + 2 \, b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{2} b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 + 12*(d*x + c)*a*b^2 + 2*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*a^2*b*sin(d*x + c))/d","A",0
472,1,73,0,0.340769," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b - 12 \, {\left(d x + c\right)} b^{3} - 36 \, 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^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2*b - 12*(d*x + c)*b^3 - 36*a*b^2*sin(d*x + c))/d","A",0
473,1,95,0,0.370716," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2} + 32 \, b^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"1/32*((12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^2 + 32*b^3*sin(d*x + c))/d","A",0
474,1,119,0,0.455235," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3,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^{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^{2} b - 480 \, {\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^{3}}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2*b - 480*(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^3)/d","A",0
475,1,145,0,0.384116," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3,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^{3} - 192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} b - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b^{3}}{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^3 - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2*b - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b^2 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*b^3)/d","A",0
476,1,275,0,0.384558," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} b + 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)} a b^{3} - 5 \, 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 \, 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^{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 \, d}"," ",0,"1/480*(640*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3*b + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a*b^3 - 5*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*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^4*(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
477,1,195,0,0.389946," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} b^{2} + 4 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} b^{4} - 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 \, a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 60 \, a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(120*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2*b^2 + 4*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*b^4 - 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*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 60*a^4*tan(d*x + c))/d","A",0
478,1,180,0,0.354561," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{3} - 3 \, 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 \, 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^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 192 \, a^{3} b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(64*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^3 - 3*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*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^4*log(sec(d*x + c) + tan(d*x + c)) + 192*a^3*b*tan(d*x + c))/d","A",0
479,1,121,0,0.389591," ","integrate((a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} b^{4}}{3 \, d} - \frac{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)}}{d} + \frac{4 \, a^{3} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{6 \, a^{2} b^{2} \tan\left(d x + c\right)}{d}"," ",0,"a^4*x + 1/3*(tan(d*x + c)^3 + 3*tan(d*x + c))*b^4/d - 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))/d + 4*a^3*b*log(sec(d*x + c) + tan(d*x + c))/d + 6*a^2*b^2*tan(d*x + c)/d","A",0
480,1,115,0,0.356283," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} a^{3} b - b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, 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)} + 4 \, a^{4} \sin\left(d x + c\right) + 16 \, a b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(16*(d*x + c)*a^3*b - b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*a^4*sin(d*x + c) + 16*a*b^3*tan(d*x + c))/d","A",0
481,1,90,0,0.337165," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 24 \, {\left(d x + c\right)} a^{2} b^{2} + 8 \, 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)} + 16 \, a^{3} b \sin\left(d x + c\right) + 4 \, 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^4 + 24*(d*x + c)*a^2*b^2 + 8*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 16*a^3*b*sin(d*x + c) + 4*b^4*tan(d*x + c))/d","A",0
482,1,102,0,0.337138," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} b - 24 \, {\left(d x + c\right)} a b^{3} - 3 \, b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, a^{2} b^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3*b - 24*(d*x + c)*a*b^3 - 3*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 36*a^2*b^2*sin(d*x + c))/d","A",0
483,1,109,0,0.457031," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4,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^{4} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} b + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b^{2} + 96 \, {\left(d x + c\right)} b^{4} + 384 \, 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^4 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3*b + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2*b^2 + 96*(d*x + c)*b^4 + 384*a*b^3*sin(d*x + c))/d","A",0
484,1,133,0,0.425247," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} b - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{3} + 120 \, b^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3*b - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^3 + 120*b^4*sin(d*x + c))/d","A",0
485,1,170,0,0.367960," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4,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^{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^{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^{2} b^{2} + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a b^{3} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{4}}{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^4 - 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3*b - 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2*b^2 + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*a*b^3 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*b^4)/d","A",0
486,1,198,0,0.359918," ","integrate((a+b*sec(d*x+c))^5,x, algorithm=""maxima"")","a^{5} x + \frac{5 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{4}}{3 \, d} - \frac{b^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{16 \, d} - \frac{5 \, a^{2} b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{2 \, d} + \frac{5 \, a^{4} b \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d} + \frac{10 \, a^{3} b^{2} \tan\left(d x + c\right)}{d}"," ",0,"a^5*x + 5/3*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^4/d - 1/16*b^5*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1))/d - 5/2*a^2*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1))/d + 5*a^4*b*log(sec(d*x + c) + tan(d*x + c))/d + 10*a^3*b^2*tan(d*x + c)/d","A",0
487,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(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
488,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(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
489,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(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
490,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
491,-2,0,0,0.000000," ","integrate(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
492,-2,0,0,0.000000," ","integrate(1/(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
493,-2,0,0,0.000000," ","integrate(cos(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
494,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
495,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(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
496,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(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
497,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(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
498,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(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
499,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(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
500,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
501,-2,0,0,0.000000," ","integrate(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
502,-2,0,0,0.000000," ","integrate(1/(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
503,-2,0,0,0.000000," ","integrate(cos(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
504,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
505,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(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
506,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(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
507,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(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
508,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(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
509,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
510,-2,0,0,0.000000," ","integrate(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
511,-2,0,0,0.000000," ","integrate(1/(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
512,-2,0,0,0.000000," ","integrate(cos(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
513,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
514,-2,0,0,0.000000," ","integrate(sec(d*x+c)^6/(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
515,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(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
516,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(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
517,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(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
518,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
519,-2,0,0,0.000000," ","integrate(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
520,-2,0,0,0.000000," ","integrate(1/(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
521,-2,0,0,0.000000," ","integrate(cos(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
522,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
523,1,47,0,0.782437," ","integrate(1/(3+5*sec(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) - 5 \, \arctan\left(\frac{\sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right) + 1\right)}}\right)}{6 \, d}"," ",0,"1/6*(4*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) - 5*arctan(1/2*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
524,1,88,0,0.449749," ","integrate(1/(3+5*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{150 \, \sin\left(d x + c\right)}{{\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 4\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - 64 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + 35 \, \arctan\left(\frac{\sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right) + 1\right)}}\right)}{288 \, d}"," ",0,"-1/288*(150*sin(d*x + c)/((sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4)*(cos(d*x + c) + 1)) - 64*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + 35*arctan(1/2*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
525,1,131,0,0.471132," ","integrate(1/(3+5*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{150 \, {\left(\frac{44 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{19 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{\frac{8 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 16} - 2048 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + 3055 \, \arctan\left(\frac{\sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right) + 1\right)}}\right)}{27648 \, d}"," ",0,"-1/27648*(150*(44*sin(d*x + c)/(cos(d*x + c) + 1) - 19*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 16) - 2048*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + 3055*arctan(1/2*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
526,1,171,0,1.127469," ","integrate(1/(3+5*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{150 \, {\left(\frac{11312 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4576 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1037 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{\frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{12 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{\sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 64} - 32768 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + 11215 \, \arctan\left(\frac{\sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right) + 1\right)}}\right)}{1327104 \, d}"," ",0,"-1/1327104*(150*(11312*sin(d*x + c)/(cos(d*x + c) + 1) + 4576*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1037*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 12*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 64) - 32768*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + 11215*arctan(1/2*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
527,1,70,0,0.483034," ","integrate(1/(5+3*sec(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) - 3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 2\right) + 3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 2\right)}{20 \, d}"," ",0,"1/20*(8*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 2) + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 2))/d","A",0
528,1,111,0,0.469845," ","integrate(1/(5+3*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{180 \, \sin\left(d x + c\right)}{{\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 4\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - 128 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + 123 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 2\right) - 123 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 2\right)}{1600 \, d}"," ",0,"-1/1600*(180*sin(d*x + c)/((sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4)*(cos(d*x + c) + 1)) - 128*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + 123*log(sin(d*x + c)/(cos(d*x + c) + 1) + 2) - 123*log(sin(d*x + c)/(cos(d*x + c) + 1) - 2))/d","A",0
529,1,155,0,0.488282," ","integrate(1/(5+3*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{540 \, {\left(\frac{156 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{49 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{\frac{8 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 16} - 4096 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + 8361 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 2\right) - 8361 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 2\right)}{256000 \, d}"," ",0,"-1/256000*(540*(156*sin(d*x + c)/(cos(d*x + c) + 1) - 49*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 16) - 4096*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + 8361*log(sin(d*x + c)/(cos(d*x + c) + 1) + 2) - 8361*log(sin(d*x + c)/(cos(d*x + c) + 1) - 2))/d","A",0
530,1,194,0,0.519608," ","integrate(1/(5+3*sec(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{540 \, {\left(\frac{26384 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16032 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2559 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{\frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{12 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{\sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 64} - 65536 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + 278151 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 2\right) - 278151 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 2\right)}{20480000 \, d}"," ",0,"-1/20480000*(540*(26384*sin(d*x + c)/(cos(d*x + c) + 1) - 16032*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2559*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 12*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 64) - 65536*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + 278151*log(sin(d*x + c)/(cos(d*x + c) + 1) + 2) - 278151*log(sin(d*x + c)/(cos(d*x + c) + 1) - 2))/d","A",0
531,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
532,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
533,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
534,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a), x)","F",0
535,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
536,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
538,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
539,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
540,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*sec(d*x + c), x)","F",0
541,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2), x)","F",0
542,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*cos(d*x + c), x)","F",0
543,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*cos(d*x + c)^2, x)","F",0
544,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
547,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
548,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2), x)","F",0
549,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c), x)","F",0
550,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^2, x)","F",0
551,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^3, x)","F",0
552,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^4, x)","F",0
553,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(7/2), x)","F",0
554,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{5}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/sqrt(b*sec(d*x + c) + a), x)","F",0
555,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(b*sec(d*x + c) + a), x)","F",0
556,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
557,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
558,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
559,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sec(d*x + c) + a), x)","F",0
560,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
561,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
562,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
566,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
567,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-3/2), x)","F",0
568,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
569,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
570,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
575,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-5/2), x)","F",0
576,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
577,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sec(d*x + c) + a)^(5/2), x)","F",0
578,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-7/2), x)","F",0
579,0,0,0,0.000000," ","integrate(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)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
580,0,0,0,0.000000," ","integrate(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)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
581,0,0,0,0.000000," ","integrate(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{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
582,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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(sec(d*x + c)), x)","F",0
583,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{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)/sec(d*x + c)^(3/2), x)","F",0
584,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{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)/sec(d*x + c)^(5/2), x)","F",0
585,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{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)/sec(d*x + c)^(7/2), x)","F",0
586,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*sec(d*x + c)^(5/2), x)","F",0
587,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*sec(d*x + c)^(3/2), x)","F",0
588,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*sqrt(sec(d*x + c)), x)","F",0
589,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/sqrt(sec(d*x + c)), x)","F",0
590,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/sec(d*x + c)^(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/sec(d*x + c)^(5/2), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/sec(d*x + c)^(7/2), x)","F",0
593,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(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(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\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)^3*sqrt(sec(d*x + c)), x)","F",0
595,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^3/sqrt(sec(d*x + c)), x)","F",0
596,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^3/sec(d*x + c)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \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)^3/sec(d*x + c)^(5/2), x)","F",0
598,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \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)^3/sec(d*x + c)^(7/2), x)","F",0
599,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
603,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^4/sec(d*x + c)^(3/2), x)","F",0
604,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a), x)","F",0
609,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
610,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
611,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
612,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
613,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
614,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(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
618,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
619,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
620,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
621,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate(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
626,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-2,0,0,0.000000," ","integrate(1/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
628,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
629,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
632,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
633,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
635,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
638,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\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)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
639,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\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)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
640,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
641,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
642,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
643,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
644,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/sec(d*x + c)^(5/2), x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/sec(d*x + c)^(7/2), x)","F",0
646,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/sec(d*x + c)^(9/2), x)","F",0
647,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
648,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
649,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
650,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
651,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
652,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
653,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
654,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
655,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
656,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
657,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
659,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
660,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
661,0,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(9/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
662,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
663,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
664,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
665,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
666,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
667,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
668,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
669,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))), x)","F",0
670,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))), x)","F",0
671,0,0,0,0.000000," ","integrate(1/(2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))), x)","F",0
672,0,0,0,0.000000," ","integrate(1/(-2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))), x)","F",0
673,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))), x)","F",0
674,0,0,0,0.000000," ","integrate(1/(3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))), x)","F",0
675,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))), x)","F",0
676,0,0,0,0.000000," ","integrate(1/(-3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))), x)","F",0
677,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{3 \, \sec\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(3*sec(d*x + c) + 2), x)","F",0
678,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{3 \, \sec\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(3*sec(d*x + c) - 2), x)","F",0
679,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(2-3*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-3 \, \sec\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-3*sec(d*x + c) + 2), x)","F",0
680,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-2-3*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-3 \, \sec\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-3*sec(d*x + c) - 2), x)","F",0
681,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{2 \, \sec\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(2*sec(d*x + c) + 3), x)","F",0
682,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(3-2*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-2 \, \sec\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-2*sec(d*x + c) + 3), x)","F",0
683,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{2 \, \sec\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(2*sec(d*x + c) - 3), x)","F",0
684,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(-3-2*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{-2 \, \sec\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(-2*sec(d*x + c) - 3), x)","F",0
685,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c), x)","F",0
686,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(1/3), x)","F",0
687,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^4, x)","F",0
688,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^3, x)","F",0
689,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^2, x)","F",0
690,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c), x)","F",0
691,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(2/3), x)","F",0
692,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(4/3)*sec(d*x + c), x)","F",0
693,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(4/3), x)","F",0
694,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^4, x)","F",0
695,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^3, x)","F",0
696,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c)^2, x)","F",0
697,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3)*sec(d*x + c), x)","F",0
698,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/3), x)","F",0
699,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(b*sec(d*x + c) + a)^(1/3), x)","F",0
700,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*sec(d*x + c) + a)^(1/3), x)","F",0
701,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(1/3), x)","F",0
702,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
703,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-1/3), x)","F",0
704,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
705,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-2/3), x)","F",0
706,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(4/3), x)","F",0
707,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-4/3), x)","F",0
708,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(5/3), x)","F",0
711,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*sec(d*x + c) + a)^(5/3), x)","F",0
712,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(5/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-5/3), x)","F",0
713,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(2/3)/(b*sec(d*x + c) + a), x)","F",0
714,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{1}{3}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(1/3)/(b*sec(d*x + c) + a), x)","F",0
715,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)), x)","F",0
716,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)), x)","F",0
717,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/3), x)","F",0
718,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/3), x)","F",0
719,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(4/3), x)","F",0
720,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3), x)","F",0
721,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
722,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(1/3), x)","F",0
723,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(2/3), x)","F",0
724,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(4/3), x)","F",0
725,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/3),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/3), x)","F",0
726,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/3),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/3), x)","F",0
727,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{7}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/3), x)","F",0
728,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/3), x)","F",0
729,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(4/3), x)","F",0
730,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(2/3), x)","F",0
731,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(1/3), x)","F",0
732,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(1/3), x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(2/3), x)","F",0
734,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(4/3), x)","F",0
735,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/3), x)","F",0
736,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/3), x)","F",0
737,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{7}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/3), x)","F",0
738,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/3), x)","F",0
739,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(4/3), x)","F",0
740,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(2/3), x)","F",0
741,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(1/3), x)","F",0
742,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(1/3), x)","F",0
743,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(2/3), x)","F",0
744,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(4/3), x)","F",0
745,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(5/3), x)","F",0
746,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/3),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(5/2)/sec(d*x + c)^(7/3), x)","F",0
747,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
748,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
749,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{4}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(4/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
750,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{2}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(2/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
751,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(1/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
752,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)), x)","F",0
753,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)), x)","F",0
754,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(4/3)), x)","F",0
755,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/3)), x)","F",0
756,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/3)), x)","F",0
757,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/3)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
758,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/3)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
759,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{4}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(4/3)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
760,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{2}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(2/3)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
761,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{1}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(1/3)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
762,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(1/3)), x)","F",0
763,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(2/3)), x)","F",0
764,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(4/3)), x)","F",0
765,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/3)), x)","F",0
766,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/3)), x)","F",0
767,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{7}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(7/3)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
768,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/3)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
769,0,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{4}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(4/3)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
770,0,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{2}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(2/3)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
771,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{1}{3}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(1/3)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
772,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(1/3)), x)","F",0
773,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(2/3)), x)","F",0
774,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(4/3)), x)","F",0
775,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/3)), x)","F",0
776,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/3)), x)","F",0
777,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{3} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^3*(d*sec(f*x + e))^n, x)","F",0
778,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*(d*sec(f*x + e))^n, x)","F",0
779,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
780,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
781,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(b \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(b*sec(f*x + e) + a)^2, x)","F",0
782,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
783,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
784,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{b \sec\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/sqrt(b*sec(f*x + e) + a), x)","F",0
785,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{n}}{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^n/(b*sec(f*x + e) + a)^(3/2), x)","F",0
786,0,0,0,0.000000," ","integrate(sec(f*x+e)^n*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
787,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
788,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
789,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
790,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
791,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m, x)","F",0
792,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*cos(f*x + e), x)","F",0
793,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
794,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(9/2), x)","F",0
795,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int {\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)*cos(d*x + c)^(7/2), x)","F",0
796,0,0,0,0.000000," ","integrate(cos(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)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
797,0,0,0,0.000000," ","integrate(cos(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)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
798,0,0,0,0.000000," ","integrate(cos(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{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
799,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{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(cos(d*x + c)), x)","F",0
800,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{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)/cos(d*x + c)^(3/2), x)","F",0
801,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{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)/cos(d*x + c)^(5/2), x)","F",0
802,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^2*cos(d*x + c)^(9/2), x)","F",0
803,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*cos(d*x + c)^(7/2), x)","F",0
804,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*cos(d*x + c)^(5/2), x)","F",0
805,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*cos(d*x + c)^(3/2), x)","F",0
806,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int {\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)^2*sqrt(cos(d*x + c)), x)","F",0
807,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/sqrt(cos(d*x + c)), x)","F",0
808,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/cos(d*x + c)^(3/2), x)","F",0
809,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\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)^2/cos(d*x + c)^(5/2), x)","F",0
810,-1,0,0,0.000000," ","integrate(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
811,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(7/2), x)","F",0
812,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(5/2), x)","F",0
813,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
814,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
815,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
816,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
818,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a), x)","F",0
819,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
820,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
821,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
822,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
823,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
824,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^2, x)","F",0
825,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^2, x)","F",0
826,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
827,-1,0,0,0.000000," ","integrate(1/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
828,-1,0,0,0.000000," ","integrate(1/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
829,-1,0,0,0.000000," ","integrate(1/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
830,-1,0,0,0.000000," ","integrate(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
831,-1,0,0,0.000000," ","integrate(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
832,-1,0,0,0.000000," ","integrate(1/(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
833,-1,0,0,0.000000," ","integrate(1/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
834,-1,0,0,0.000000," ","integrate(1/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
835,-1,0,0,0.000000," ","integrate(1/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
836,-1,0,0,0.000000," ","integrate(1/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
837,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
838,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
839,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
840,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
841,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
842,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*cos(d*x + c)^(7/2), x)","F",0
843,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*cos(d*x + c)^(5/2), x)","F",0
844,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
845,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
846,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
847,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^(9/2), x)","F",0
849,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^(7/2), x)","F",0
850,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^(5/2), x)","F",0
851,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*cos(d*x + c)^(3/2), x)","F",0
852,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
853,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
854,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
855,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
856,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
857,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
858,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
859,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
860,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
861,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
862,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
863,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\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(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(3/2), x)","F",0
865,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
866,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
867,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
868,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
869,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\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(cos(d*x + c)^(3/2)/(b*sec(d*x + c) + a)^(5/2), x)","F",0
870,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a)^(5/2), x)","F",0
871,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
872,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
873,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
874,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*sec(d*x + c) + a)^(5/2)*cos(d*x + c)^(7/2)), x)","F",0
875,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{3} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^3*(d*cos(f*x + e))^n, x)","F",0
876,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*(d*cos(f*x + e))^n, x)","F",0
877,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*(d*cos(f*x + e))^n, x)","F",0
878,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
879,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^n/(a+b*sec(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{n}}{{\left(b \sec\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^n/(b*sec(f*x + e) + a)^2, x)","F",0
